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Catalog No.AP5939
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Publication No. 5939
Measurement Challenge
A Density Laboratory Kit
Introduction
Take the measurement challenge! Accurately estimate the length, width, and height of a small plastic block and
calculate the block's volume. Then predict the mass of the block without a balance by using the block's known
density. Repeat this process with a second measurement device. Which form of measurement is more accurate?
Concepts
• Measurement
• Significant figures
• Estimations and cert ainty
• Volume, mass and density
Background
All measurements involve some degree of error or estimation. The measurements are based on the fact that the hum an
eye can estimate to one-tenth of the smallest mark shown on a measuring instrument. Therefore, a ruler with only 1- cm
increments shown can provide measurement s that are estimated to 0/1 cm, while a ruler with a 0.1 increments shown can
provide measurements that are estimated to 0.01 cm.
I n this activity, the fir st go al is to d eter mine the vo lume o f a p lastic b lo ck. T he vo lume o f any regular
so lid can be calculated using Eq uatio n 1. The length, wid th and height must b e estimated using a reliable
measuring instr ument.
Volume = Length x Width x Height
Equation I
Once the solid’s volume has been calculated, the mass can be predicted using the known density value of the solid. To
predict the mass, rearrange the density equation shown in Equation 2 to solve for mass, as shown in Equation 3.
Density = Mass/Volume
Mass = Volume x Density
Equation 2
Equation 3
Success of this laboratory activity depends on the ability to take accurate measurements to make valid estimations and to apply the rules
for significant figures in mass and volume (and density) calculations.
Pre-Lab Activity -Length and Area
Materials
(for each lab group)
Calculator
Metric ruler, 0.1 cm markings
Procedure
Reading the Metric Ruler
1. Obtain a metric ruler. Take a close look at the markings on the ruler. What is the distance between the smallest
markings? Obtain a micrometer. What is the distance between the smallest markings on the micrometer.
2. It is generally accepted that scientific measurements can be estimated to one-tenth of the smallest mark on the
instrument.
Therefore, if a ruler has a marking every 1 cm, a person can reliably estimate to the nearest 0.1 cm. Likewise, if a
ruler has a marki ng every 0.1 cm, a person can reliably estimate to the nearest 0.01 cm. With the metric ruler
provided by your instrctor, what is the most reliable estimation that can possibly be made?
3 Use the metric ruler to measure the length of the following line segments. Be sure to estimate to the hundredth s place for
each measurement. Be sure to include the appropriat e units for length. Underl ine the digit that you estim ated while
measuring.
Measure These Line Segments
Ruler Measurement
Measurement calipers
a.
b.
c.
Applying Significant Figures in Calculations
4. Use the metric ruler a n d c a l i p e r s to mea sure the length and width of each of the rectangles below. Be sure to
estimate to the proper decimal place for each measurement and to include units with each measurement. Underline
the digit that you estimated while measuring.
Rectangle #1
Rectangle #2
Length:
_
Length:
Width:
_
Width:
_
_
5. To calculate the area of the rectangles, multipl y the length by the width. Round the area values to the proper number of
significant figures. Be sure to include the appropriate units for area.
Area of
Rectangle #1:
_
Area of
Rectangle #2:
_
Experiment #1 -Density Calculation
Materials
(for each lab group)
Balance
Metric ruler, 0. 1 cm markings
Calculator
Plastic blocks, 1
Procedure
I. Obtain a plastic block from your teacher. Record the block number and color of the bl ock in the table below.
2. U se the l abora tory balance to measure the mass of the block. Record the mass in the data table.
3. Use the metri c ruler to mea sure the dimen sions of the block . Record these values in the data table.
4. Calcul ate the vol ume of the block u sing Equat ion I from the background informat ion. Round the answer to the proper
number of si gnificant figures. Record the volu me i n the d ata table. Be sure to include the appropriate unit s.
5. Calculate the density of the plastic block u sing Equati on 2 from the background informat ion. Record the density in the
data table. Be sure to includ e the appropriate units.
6. R epeat steps 1 -5 for two additional block s, being sure to obtain blocks of different colors. R ecord all data in the table
below.
7. Check with your instru ctor to determ ine the accu racy of your measurem ent s and calcula tions.
Data Table
Block N umber
Color of Block
Mass (g)
Length (cm)
Width (cm)
Height (cm)
Volume (cm 3)
Density (g/cm 3)
-3 -
IN5939
ID 2007 Flinn Scientific. Inc. A ll Right s Reserved.Reproduction permission is granted only to >Cicncc teachers who have purcha<cd Mc:l\uremenl Challenge, Catalog No. A P5939, from Flinn
Scient ific. I nc. No pan of t h i' ma t erial may be reproduced or 1rnn mit1ed i n any form or by any mean :,, electronic or mechanical. including. but not limi 1cd 10 pho1ocopy. recording. or any in formation
'\torngc a nd rc1ricval y,r cm , wi 1hou1 permision in writ ing from Flinn Scientific. Inc.
Experiment #2 -The Measurement Challenge
Materials
Balance
Metric ruler, 0.1 cm markings
Calculator
Plastic block
Procedure
I. Obtain a plastic block from your teacher. Record the block number and color of the sample. The block number must be
different from an y of the block numbers used in Experiment # 1 .
Color of Block:
Block Number:
_
2. Measure the dimensions (length, width, and height) of the block. Be sure to estimate all measurements to the correct deci­
mal place and to include unit s with each measurement.
Length:
Width:
_
_
H eight:
3. Calculate the volume of the block using Equation l. Round the answer to the proper number of significant figures. Record the
volume in the data table. Be sure to include the appropriate units.
Volume:
_
4. Use the known density value to predict the mass of the plastic sample. The known density values for each different type of colored
plastic are shown in the table below.
Color of Block
Density (g/cm3)
Paper white
0.51
B lack
0.96
Milky-white
0.9 1
Clear
1.17
Gray
1 .4 1
Predict ed Mass of Block:
_
When the mass of the plastic block has been calculated and a prediction made, bring the block to the teacher. The teacher wi ll
measure the actual mass of the block using a laboratory balance.
Actual Mass Measurement:
_
Teacher Initials:
_
(To be filled in by the teacher)
5. Determine the accuracy of the mass calculation by comparing the predicted (calculated) mass with eactual (measured) mass.
Calculate the percent error (or difference) in the mass calculation using the equation below.
Percent Error
= I Calculated Mass
- Actua l M ass
Actual Mass
-4© 2007 Fli nn Scientific, I nc. All Rights Reserved. Rcproduc1ion pcrmi !<-ion is grnntcd only
Ix
1 00
IN5939
science 1cachcrs who have purchased M easurement Challenge, Catalog No. AP5939, from Flinn
Scicn1ific. I nc. No pan of th is rmucrial may be reproduced or 1ran mi11cd in any form or by any mean . electronic or mechanical. including, bu t 001 limited to phorocopy, recording. or any information
storage and rctricv<1I syMcm. without pcrm i!\!\ion in wriling from Flinn Scicn1ific. Inc.
10
Repeat the above using calipers for the second time.
Block N umber:
Color of Block:
_
6. Measure the dimensions (length, width, and height) of the block. Be sure to estimate all measurements to the correct deci­
mal place and to include unit s with each measurement.
Length:
_
Width:
_
H eight:
7. Calculate the volume of the block using Equation l. Round the answer to the proper number of significant figures. Record the
volume in the data table. Be sure to include the appropriate units.
Volume:
_
8. Use the known density value to predict the mass of the plastic sample. The known density values for each different type of colored
plastic are shown in the table below.
Color of Block
Density (g/cm3)
Paper white
0.51
B lack
0.96
Milky-white
0.9 1
Clear
1.17
Gray
1 .4 1
Predict ed Mass of Block:
_
When the mass of the plastic block has been calculated and a prediction made, bring the block to the teacher. The teacher wi ll
measure the actual mass of the block using a laboratory balance.
Actual Mass Measurement:
_
Teacher Initials:
_
(To be filled in by the teacher)
9. Determine the accuracy of the mass calculation by comparing the predicted (calculated) mass with eactual (measured) mass.
Calculate the percent error (or difference) in the mass calculation using the equation below.
Percent Error
10.
= I Calculated Mass
- Actua l M ass
Actual Mass
Ix
1 00
Which of the two methods of measurement proved to be more accurate? Why?
Teacher's Notes
Measurement Challenge Kit
Materials Included in Kit
Plastic blocks, different densities and colors, 30
Additional Materials Needed (for each lab group)
Metric ruler, 0.1 cm markings
Balance
Calculator
Connecting to the National Standards
This laboratory activi ty relates to the follow ing National Science Education Standards ( 1996):
Unifying Concepts and Processes: Grades K-12
Systems, order, and organ izati on
Evidence, model s, and explanati on
Cont ent Standards: Grades 5-8
Content Standard A: Science as Inquiry
Content Standard B: Physical Science, properties and changes of properties in matter
Content Standards: Grades 9-12
Content Stand ard A: Science as Inquiry
Content Standard B : Physical Science, structu re and prop erties of matter
Tips
• This laboratory kit contains enough material s for u nlimited u se by a class of 30 students. The activities can be performed
in a stand ard 50-m inute lab peri od.
• Experiment # 1 may be used as a traditional classroom density experiment. A ll students can start with Experiment # I and
then go on to do either Experiment #2 or #3.
• Experiments #2 and #3 serve as hi gher-level authentic assessment labs for the determin ation of den sity. Each student
should receive hi s or her own plastic density block so that each student i s held accountab le. Be sure the bl ock number is
different than the one used in Experiment #1.
• Measurement errors include limitati ons of the ruler (thickness of the ruler, line width, systematic error, etc.) and the human
eye (studen ts with sight problems, parallax , random error, etc.).
• There is a large normal va riatjon in the density of each plasti c. In contrast to the density of a pure substance, such as copper,
which can be known with a hi gh degree of accuracy, the density of a plastic materi al depends on the molecu l ar weight of the
polymer, the degree of branching in the polymer chain , the presence of fillers, etc.
• The identity and density range for each plastic are shown below.
Color
Wh ite
Identity
Sintra
Density Range (g/cm 3)
0.48-0.54
Percent Uncerta inty
5.8%
Black
High-density Polyethylene
0.94-0.98
2. 1%
Milky white
Polypropyl ene
0.89-0.93
2.2%
Clear
Acry lic
l.13-1 .2.1
3.4%
Gray
Polyv inyl Chloride
J.36-1.46
3.5%
-6© 2007 Flinn Scientific, Inc. All Rights Reserved.
J N5939
Teacher's Notes continued
• The expected percent error in the mass calculation s for Experiments #2 and 3 depends on the material. The largest percent
error will probabl y be found for th e paper-white Sintra blocks becau se the relative uncertainty in the den sity is (0.03/0.51) x
I 00 or 6%.The percent un certa inty in the density for each plasti c is shown above.
• Sintra is an "expanded " polyvinyl chl oride (PVC). The density of the Sintra block s may change over tim e due to outgassing
or compacting.
• Block dimensions vary sligh tly from kit to ki t. Therefore, exact dimensions for each block are not provided for the teacher.
It i s su gges1ed 1ha1 an independen1 "master measurement sheet" be made for each block provided in the kit prior to class.
Teachers may wish to number the bl ock s from I to 30 when creating a key. It wi ll take about an hour to mea sure the dimen­
sions, wei gh the bl ocks, and calculate the volumes and densities for all 30 bl ocks. After students ha ve compl eted their
measurements and calculation s, coll ect and ent er the stud enl data into a spreadsheet. Standard deviations and the effects of
mea surement error can then be revea led . The large pool of data may make it helpful to determine th e "acceptable" error for
each of the five types of blocks.
Introducing Experiment #1 - Density Calculations
• Give each student only pa ges J -3 of the handout-Expe rim ent # J. Do not hand out Experiment #2 or #3 yet since the pur­
pose of Experim ent # I is t o determine density, and Experiments #2 and #3 supply the known densities.
• Student s will determine the densi ty of three plastic block s. Give each stud ent one block to start. Wh en done with the first
block , have the student return die block 10 you i n exchange for a second bl ock and then a third block , each should be a dif ­
ferent color. Do not allow studems 10 simpl y trade block s on their own since the goal i s to learn to measure and calculate,
and studenl s may be tempted to share measuremenl daia.
• Students should be comfortable with reading a ruler t o the proper number of digits. R emind stud ents that they should be
able to estim ate !heir measurements 10 the hundredth s pl ace with rulers that ha ve m arkings every 0.1 cm .
• The pre-laboratory activity wi ll hel p to reinforce the proper u se of rulers and estim ating to the appropriate num ber of si g­
nificant d igits. The recommended sequence is su ch that stud ent s progress from measurin g the l engths of line segments to
determinin g the area for rectan gles and fin ally to determ i nin g the vo lume of the block s. Thi s sequence allows the student s
to advance from simple one-dimensi onal measuremems to t wo- and three-dimensional calculations.
• In grading the accu racy of the predicted mass of different block , please keep in mind the percent uncert ainty in the average den­
sity of each plastic.
• Teachers ma y wi sh to use Experiment # I as a tradition a l den sity experi ment where student s become profici ent in the
proper u se of laboratory balances, rul ers, and density ca lculations. Students often experi ence difficulty initially with dis­
tingui shin g between the related term s of mass, volume. and density . Teachers should emphasi ze these defi nitions so that
stud ents u se these sci entific t erm s properly.
Introducing Experiment #2 or #3 -The Measurement Challenge
• Each stud ent should be given a copy of either Experim ent #2 or Experim ent #3. Whil e both experiments are hi gh level,
teach ers wh o prefer a more open-ended approach may wish to u se Experim ent #3, w hich forces stud ent s to pl an their own
mathemati ca l strategy. Tell studen ts th at the overall goal in either experim ent is to u se a ru ler and the kn ow n density va lues
to predict the mass of their plastic bl ock. Thi s should be clearly stated to clarify the students' task.
• Each student should be given a rul er and one pl ast ic bl ock sampl e with a different bl ock number from that u sed in
Ex periment # 1. The block s should be distributed so thal stud ent s receive allernating colors. By vary ing the colors of the
samples, die students are less likely to compare answers w i1h the other stud ent s sitting near them. Remind student s that each
color of plastic ha s a different density va lue, which will impact their eventu al ma ss calculations.
• Remind stud ents that they wi ll be as essed on the accuracy of their pred icted mass to the actual ma ss. Student s frequently
incorrectl y label their calculated volume as bein g their bl ock 's mass. Caution them about thi s error.
• Teachers are encouraged to stand at the labora tory ba l ance while stud ent s are measurin g the dimensi ons of the plastic
block s. Student s may be tempted to gain an advanta ge (i .e., cheat) by measurin g the actual mass of the ir pl astic sample if
they have easy access to any laboratory balances!
-7© 2007 Flinn Scient ific, I n c.A ll Rights Reserved .
IN5939
Teacher's Notes
continued
Sample Answers to Pre-Lab Activity
Reading the Metric Ruler
l . Obtain a metric ruler.Take a close look at the markings on the rnler. What i s distance between the smallest markings on the ru ler?
Answer:
The smallest markings on the ru l er are 0. 1 cm.
2. It is generally accepted that scientific measurements can be estimated to one-tent h of the smallest mark on t he i nstrum ent.
Therefore, i f a rul er has a marking every I cm, a person can reliabl y estim ate to the nearest 0.1 cm. Li kewi se, if a ru ler
has a markin g every 0. 1 cm, a person can reliably estim ate to the nearest 0.01 cm . Wi th the metric ru ler prov ided by your
instructor, wh at is the most reliabl e esti mation that can possibly be m ade?
A nswer: A ru ler wi th markin gs every 0. 1 cm provides measu rements to the nearest 0.01 cm.
3. Use the metr ic ruler to measure the length of the follow i ng line segment s. Be su re to esti mate to the hundred ths place for
each measu rement. Und erline the d igit that you estimated.
Answer:
Measurement ran ges are given below. Answers may va ry becau se of t he li mitiatio n s of the ruler and of the
hum an eye. The l ast digit is underlined because thi s the the estimated d igit and may vary.
Line a = 2.8Q-2.9Q cm
Line b
=
1 .3.5.-l.4.5. cm
Line c = 3.6.5.-3.7.5. cm
Applying Significant Figures in Calculations
4. Use the metric rul er to measure the length and width of each of the rectangles below. Be su re to est i mate to the proper
decimal pl ace for each measurement and to in clude units wit11 each measurement.
Answer:
Measurement ranges are gi ven bel ow. An swers may va ry becau se of the l i mi t i ations of the ru ler and of the
hu ma n eye. The last digi t i s underlin ed becau se this the the estim ated digit and may vary.
Rectang l e # I : Length
=
Rectangle #2: Length
4.8 -4.9.5. cm; Width
2.9Q-3.0Q cm
8.0Q-8. lQ cm ; Wi dth
2.0].-2. 1.5. cm
5. To calcul ate the area of the rectangl es, multiply the length by the w idth. R ound the area va l ues to the proper number of
sign ificant figures. Be sure to include the appropriate units for area.
An swer:
Measurement ranges are gi ven below. An swers may vary because of the lim i tiations of the ruler and of the
hum an eye. The last digit is underlined because this the the estim ated d i gi t and may vary.
Rectangle# I :Area
Rect angle #2: Area
14.1-14.2
=
16.1- 17.1
Acknowledgment
Special thanks to Jeff Bracken , chemi stry teacher at Westerville N orth High School , Westervi lle, OH for devel opin g this
uniqu e and ingeniou s laboratory acti v ity.
Reference
Plum sky, R . J. Chem. Ed uc. 1996, 73, 451-454.
The Measurement Challenge-A Density Laboratory Kit is available from Flinn Scientific, Inc.
Catalog No.
AP5939
AP5387
Desc ription
Measurement Challenge-A Density Laboratory Kit
Rulers, Metric/English,Clear
Consu lt your F/i1111 Scie111ific Caralog/Refere11ce Ma1111a/ for current prices.
-8© 2007 Flinn Scientific, I nc. All R igh1s Reserved .
IN5939
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