SCIENTIFIC THINKING in EXPERIMENTAL SETTINGS
An experimental design unit made for the freshman physics class by Kathy Malone, Kamille
Johnson Harless, Anita Schuchardt, Bill Diehl, and Dudley Parr at Shady Side Academy. This is
very much a team effort! (This is the first draft, spring 2006.) This forms the basis for a oneweek introductory Modeling Workshop for all teachers of science and mathematics, grades 8 to
12. Also included in the workshop is constant velocity kinematics. Kathy Malone led this
workshop twice at Briarwood Christian School in Birmingham, Alabama. It was well-received!
Contact klmalone60@GMAIL.COM. Kathy Malone, Ph.D., Asst Prof. at the Ohio State
University starting in 2014 (formerly Science Department Head, Shady Side Academy,
Pittsburgh, PA 15238).
INSTRUCTIONAL GOALS
1. Experimental design
Build a qualitative model
Identify and classify variables
Make tentative qualititative predictions about the relationship between variables
2. Data Collection
Select appropriate measuring devices
Consider accuracy of measuring device and significant figures
Maximize range of data
3. Mathematical Modeling
Learn to use Graphical Analysis (Vernier) software
Develop linear relationships
Relate mathematical and graphical expressions.
Validate pendulum model
4. Lab Report
Present and defend interpretations.
Write a coherent report (See Appendix for suggested format.)
5. Graphing Misconceptions shown by freshmen
1) Origin is not 0,0
2) Counting boxes to determine slope, but not relating to units.
a. i.e. 3 boxes up/1 box over = slope of 3
3) Drawing best-fit line between two points and ignoring rest
a. Instead of drawing line that is equidistance from all points, but may not go
through any of them
4) Insisting best-fit line must go through the origin
5) Calculating slope from the data points instead of reading off the best-fit line
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6) Saying that the slope between the two farthest data points will be different from that
between two closer data points
a. We had to draw some triangles to show this
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LAB NOTES & INSTRUCTIONAL COMMENTS
I.
Helicopter lab - Experimental Design – two days only to complete
APPARATUS-- Helicopter lab
2 sizes of note cards
paperclips
meter sticks
tape
stopwatch
PRE-LAB DISCUSSION -- Helicopter lab
 Show how to make one—make sure it’s a bad one
 Ask students to think about what changes one could make to produce a more “effective”
helicopter
LAB PERFORMANCE NOTES -- Helicopter lab
 Don’t go into much detail about how to do the lab
o Tell them to record as much as they need
o Students should take raw data of each trial
o Record observations and notes
POST-LAB DISCUSSION – Helicopter lab
 Whiteboarding is introduced: tell them they need to put on the whiteboard what is
needed to show others what they concluded and why
 Be sure after presentations discuss what makes a good whiteboard – what was missing
that would have been helpful
o Discuss how they know if helicopter is better then others: need to talk about
consistency of measurements to allow comparison. Multiple trials, overall ideas
about experimental design, ask which variable allowed for most of the change if
they changed more than one variable at a time, how we could find what variable
lead to greater effectiveness
 Talk about parts of experimental design
i. Independent variable
ii. Dependent variable
iii. Control (1st trial)
iv. Controlled variables
v. Deal with why we do more than one trial if it comes up
 Lab Report: introduce report sections
b. purpose
c. Procedure: what, when, who, and why did you do it
d. data
e. Conclusion: which helicopter was the most effect and why?; What were the
similarities and the differences between groups; what would you change and what
did you learn?
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II.
Homework:
a. What was the iv in your lab? What was the DV? What were the constant
variables? Did you use a control? Why might you want to use a control? Why is
it a good idea to take more than one trail? Why might it be good to average the
data obtained?
b. Experimental Design: Problem Set #1
c. Problem Set #2
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II.
Inertial Balance Lab
APPARATUS-- Inertial Balance La
Inertial balance
Tape
c clamps (or equivalent)
stop watches
balance for mass measurement
graph paper for initial graph sketches
PRE-LAB DISCUSSION -- Inertial Balance Lab
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Show the students the inertial balance (I would not call it by its name) and how it
operates. Ask them to brainstorm what factors or variables might affect the
motion of the device. They may come up with some or all of the following:
weight in the tray, hardness with which device is clamped down, further you pull
it back, stiffness of metal bars, push up and down, where clamp the wood down,
length of metal strips, thickness of the metal strips, and amount of force used to
pull it back (same as further you pull it back)
List factors on board and discuss which ones you could effectively measure (i.e.,
what should be the independent variable). For example, can’t change the
stiffness, thickness, and length of the metal strips; push up and down really had no
effect, decided can’t measure clamping hardness easily. Mention that the factors
can’t control you want to keep them constant.
What should you measure to see if the factors affect the motion (i.e., what should
be the dependent variable)
How should we design the experiment? Looking for what to hold constant. What
could we do to be sure that the distance is pulled back the same each time? How
many trials should we use? How should we record the trials? (tables) Should we
find the average of the the trials? How many changes of the iv should we make?
What should we do with your data once we get it? What would be a nice way to
display it?
Ask them to pre lab purpose, procedure (in group work on initial procedure), and
record raw data in the lab book (on left hand side). Have them note any changes
to the procedure as they conduct the lab. Rough table for raw data.
LAB PERFORMANCE NOTES -- Inertial Balance Lab
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
Lab Hints: If they are using the hacksaw blade balance which has a holder on the
end, have the students use a balance to measure the mass to the nearest gram. If
they use the heavy-duty double blade apparatus, load the tray with standard lab
masses. Increase mass in 50g increments.
Suggest that they record the mass in kilograms (otherwise, the slope they obtain is
so small they tend to think it should be zero).
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
Below is the graph students should produce from the data obtained at this station.
TIME
MASS
Actually, the graph is slightly parabolic, but since the variance in the masses used is relatively
small, the section of the parabola obtained appears very much linear.
ANALYSIS OF DATA-- Inertial Balance Lab
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At least some groups should report a graph on the white broad since discussed in the
pre lab. I would suspect few would do y = mx + b.
They should be able to use their data to predict what would happen if the mass were
doubled.
Need to bring out what the y-intercept means? At zero grams why does it have a
period?
POST-LAB DISCUSSION -- Inertial Balance Lab
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Review in detail how to make a graph. Have all the students complete a graph and
determine the algebraically representation. Have the kids graph the results by hand
(each person in the group should have a graph which they can compare with their
other group members). May want to discuss how to set the range on the x and y axis
and that independent goes on the x axis while dependent goes on the y axis.
Discuss range of data as an experimental technique and what could we do to check if
this is really a linear graph? Put an extra large mass on the apparatus. For Example,
students did 50, 100, 150, 200, 250, 300 then they could try 1000g
In a post lab summary: discuss class consensus on verbal representation, graphical
representation, and algebraically representation.
After the students have reported the results of their experiments and their efforts to
write equations to model the relationships they have found, it is worthwhile to check
to see if they can apply the general relationships by making simple predictions.
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III.
Ball Drop Lab I (mass vs time of fall)
APPARATUS-- Ball Drop Lab I
Balls of varying masses (can ask kids to bring in some balls) – could get
some tennis balls and cut tops out to add masses to them? – or just
drop masses
Stopwatches
Meter sticks
Tape
Balance
Cushy stuff to cushion the masses
PRE-LAB DISCUSSION -- Ball Drop Lab I
o Initial question: what factors might affect how a ball drops? Demo a ball
dropping.
o They might come up with: mass, height at which you drop it, gravity, wind, and
air pressure, Rotation of mass, Air temp, Ht, Surface falling towards, Shape (open
book vs closed), Rough surface of object, Material made from (flimsy), Where is
it dropped (on moon, etc ) >>> gravity, Altitude of room (elevation), Strength of
person dropping, Friction between person’s finger and object, Static in person’s
fingers, Hemisphere we are in , Throw it instead of dropping it (could be flippey),
Wind speed air density, Color of mass, Slot or not, Weight, and Number of
computers on
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List factors on board and discuss which ones you could effectively measure (i.e.,
what should be the independent variable). Will probably have mass and height as
an option so we can say that we will look at mass first then do a separate lab for
height.
What should you measure to see if the factors affect the motion (i.e., what should
be the dependent variable)
How should we design the experiment? Looking for what to hold constant. How
many trials should we use? How should we record the trials? (tables) Should we
find the average of the trials? How many changes of the iv should we make?
What should we do with your data once we get it? What would be a nice way to
display it?
Ask them to pre lab purpose, procedure (in group work on initial procedure), and
record raw data in the lab book (on left hand side). Have them note any changes
to the procedure as they conduct the lab in their lab book. Rough table for raw
data.
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LAB PERFORMANCE NOTES -- Ball Drop Lab I
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The students may want to use more than one stopwatch (i.e., two people timing)
to get better results.
Since we recorded the mass in kilograms could do it again here but may want to
go with grams since the balls probably won’t be really high – unless we could
find a medicine ball (that would be neat).
The slope of the graph should be a straight line with a zero slope – or close too it.
They should plot this by hand
The relationship should look like:
ANALYSIS OF DATA-- Ball Drop Lab I
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
At least some groups should report a graph on the white broad since discussed in the
pre lab. I would suspect few would do y = mx + b. But the m value they calculate
should be very small.
Need to bring out what the y-intercept means? What does that mean if you double the
mass? At zero grams why does it have a time of fall (i.e., simply because the minute
you have a mass it would fall at the time they found – this is what is called a
discontinuous function in math. Therefore, no time at 0 but one directly afterwards?
POST-LAB DISCUSSION -- Ball Drop Lab I
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
May want to review how to make a graph. Have all the students complete a graph
and determine the algebraic representation if they did not do it before. Have the kids
graph the results by hand (each person in the group should have a graph which they
can compare with their other group members). May want to remind them about the
range since if they don’t start from zero time and just zoom into the values then they
could get something that looks linear even through the slope is very small.
Discuss range of data as an experimental technique and what could we do to check if
this is really had a slope of zero? Drop an extra large mass
In a post lab summary: discuss class consensus on verbal representation, graphical
representation, and algebraically representation.
After the students have reported the results of their experiments and their efforts to
write equations to model the relationships they have found, it is worthwhile to check
to see if they can apply the general relationships by making simple predictions
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IV.
Ball Drop Lab II (height vs time of fall)
APPARATUS-- Ball Drop Lab II
Balls of varying masses (can ask kids to bring in some balls) – could get
some tennis balls and cut tops out to add masses to them? Or just
drop masses
Stopwatches
Meter sticks
Tape
Balance
Cushy stuff to cushion the masses
PRE-LAB DISCUSSION -- Ball Drop Lab II
o If already mentioned height in ball drop lab I then we can go straight into
discussing experimental design.
 What should you measure to see if the factor affects the motion (i.e., what should
be the dependent variable)?
 How should we design the experiment? Looking for what to hold constant. How
many trials should we use? How should we record the trials? (tables) Should we
find the average of the trials? How many changes of the iv should we make?
What should we do with your data once we get it? What would be a nice way to
display it?
 Discuss the range of data needed? (small to very large) and How do we measure
the time? (should say stopwatch)
LAB PERFORMANCE NOTES -- Ball Drop Lab II

Try with the class to measure the time for a drop from a very small height.
Discuss what happens to the quality of the time data?
POST-LAB DISCUSSION -- Ball Drop Lab II
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Discuss limitation of stopwatch
Maybe in future we could do this if we had something to measure time accurately
(some students might suggest using computer for timing)
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V.
Circle Lab Activity
APPARATUS—Circle lab
Circles
Graph paper
string
rulers
PRE-LAB DISCUSSION -- Circle lab
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Ask them to brainstorm what factors or variables might change as the diameter of
a circle changes. Should come up with circumference, area, thickness of the
circle. Are could just assign them to find relationship between area and radius (or
diameter) and same for circumference (circumference vs diameter = 3.14)
Discuss which items to include in the lab (each group will do all of the three
above)
Ask the students to collect data without calculating the area or the circumference
using math formulas.
Discuss possible methods of finding area and circumference without using a
formula – or do we want them to do this in groups with no input from us?
LAB PERFORMANCE NOTES -- Circle Lab II
 The area is a bit difficult but can be estimated in larger chunks rather then
counting all of the squares from the paper
ANALYSIS OF DATA-- Circle Lab II
 After the students hand draw graphs you can introduce Logger Pro for data analysis
 The students can print out data tables and graph to glue into lab notebook
 Discuss why we linearize the graph and show them how to do it on Logger Pro
 Discuss how we can linearize the line using the calculated column and squaring the
area.
 Discuss the five-percent rule for intercepts. Derive the mathematical model from the
graphical representation.
POST-LAB DISCUSSION -- Circle Lab II
 Have students whiteboard results and specifically the procedure needs to be
discussed if we turn them loose.
 Emphasize need to have adequate data quantity and adequate data ranges to get
good graphs and to make conclusions.
• Discuss graphical versus mathematical models. Show samples of curve fitting.
Discuss the five-percent rule for intercepts. Derive the mathematical model from the
graphical representation.
• Reiterate the concepts of dependent and independent variables.
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VII. PENDULUM LAB ACTIVITY – LAB PRACTIUM
APPARATUS-- Pendulum Lab
masses for bobs (≈ same size and shape, different masses- you can use metal
spheres or film canisters filled with "BBs".)
string
pendulum support and clamp (or equivalent)
stop watches
balance for mass measurement
Graphical Analysis (optional)
PRE-LAB DISCUSSION -- Pendulum Lab
•
•
•
•
Set up a support stand from which at least two pendula are swinging. Ask for
observations. Request a list of factors that might have an impact on the behavior of
the pendula. Accept all suggestions at first; cull from this list those factors which are
not quantifiable (shape of bob or material) or over which you have little or no control
(room temperature, gravity). Ask which observations are related in order to isolate
dependent and independent variables.
Tell the students that for the lab practicum they will make the dependent variable the
period of swing (T). Use period rather than frequency to simplify the data analysis,
1
since T a l and f a
. The dependent variable will be graphed on the vertical
l
axis.
Tell the students that the independent variables are:
length (l).
mass (m). You should draw a distinction between mass and weight.
amplitude (A). You can measure as an angle or a distance from the rest point. (I
would say let each group decide how they will measure the amplitude)
Ask the students to make tentative predictions about how changes in the independent
variables will affect the period.
LAB PERFORMANCE NOTES -- Pendulum Lab
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•
•
•
•
Let the student groups complete and design the experiment.
Be sure to remind students that part of the grade is their observations, rough data,
rough procedure and rough predictions not only the final written lab report.
Hopefully the students will emphasize that there must be separate experimental
designs for each independent variable.
Hopefully the students will be utilizing large ranges of data otherwise, students might
conclude that the relationship is linear.
Hopefully the students will record data involving each variable separately.
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Fig. 1
Fig. 2
Fig. 3
ANALYSIS OF DATA
The students should analyze the data in Logger Pro and linearize the length vs period
data. All three graphs should have an algebraic relationship associated with them.
All of the groups should use the correlation to justify linear fit and the 5% rule.
POST-LAB DISCUSSION -- Pendulum Lab
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•
•
Focus discussion on the scientific method and experimental design
Emphasize need to have adequate data quantity and adequate data ranges to get good
graphs and to make conclusions.
Discuss graphical versus mathematical models. The students should on their
whiteboards show samples of curve fitting, discuss the five-percent rule for
intercepts, derive the mathematical model from the graphical representation.
LAB PRACTICUM – VLP (VERY LARGE PENDULUM)
Students need to figure out the period of the pendulum using their equation by only
knowing the length of the pendulum.
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