Bio A. Lab 1. Vitruvian Man Meets the Scientific Method Writing
and Testing Appropriate Hypotheses
Leonardo da Vinci’s drawing Vitruvian Man shows how the proportions of the human
body fit perfectly into a circle or a square. This diagram by Leonardo da Vinci is an
illustration of Vitruvius’ theory. According to Vitruvius’ theory the distance from
fingertip to fingertip (arm span) should be equal to the distance from head to heel
(height). In this activity you will explore the legitimacy of Vitruvius’ theory by
developing a hypothesis regarding Vitruvian Man.
A hypothesis is a possible explanation for a set of observations or an answer to a
scientific question. A hypothesis is useful only if it can be tested. Testable hypotheses are
generally written in a formalized format using an if-then statement. For example;
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If my car does not start because the battery is dead, then when I replace the old
battery with a new one, it will start.
If increasing physical activity causes a person to burn calories and lose weight,
then I should lose weight when I run 2 miles a day.
Formalized hypotheses contain both a dependent and an independent variable. The
independent variable is the one that you change and the dependent variable is the one you
observe and measure to collect data. Consider a hypothesis that says “If the temperature
is decreased, then the lizard will take longer to travel from point A to point B”. In this
example, temperature is the independent variable because the experimenter controls it
and time is the dependent variable because the time required for movement is being
measured. Using the if-then format forces the scientist to think about what results are
expected.
PURPOSE
In Part I you will develop and test a hypothesis regarding Vitruvius’ theory on human
proportions. In Part II, you will devise and test a hypothesis concerning the relationship
between foot and forearm lengths. Only Part II needs to be in your lab book.
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PRELAB ACTIVITIES:
Read the entire lab. Follow directions on the Bio A Journal Set-Up page (at the end of
the lab) Follow it with a prediction and define an appropriate margin of error. (both at
the bottom of this page). Set up your lab notebook for part II ONLY, based on the
directions at the end of this lab and using the setup for part 1 as a model.
MATERIALS
Each lab group will need the following:
calculator, meter sticks (on the wall), tape measures, ruler (used to mark height)
PROCEDURE
PART I
1. Write a hypothesis based on Vitruvius’ theory relating arm span and height. Record
your hypothesis on your student answer page in the space labeled Hypothesis #1.
2. Working with a partner, measure your arm span by standing against a flat surface and
spreading your arms out as far as possible. Using the string, have your partner
measure the distance from the longest finger on one hand to the tip of the longest
finger on the other hand across your back. Measure this length using a measuring
stick (you must decide as a class what to use). Record your measurements in Data
Table 1.
3. Repeat step two by completing a measure of arm span of your partner. Record this
result as well
4. Remove your shoes and have your partner measure your height as you stand against a
flat surface. Measure the distance from the top of your head to the floor with the
string. Measure this length with the meter stick. Record your measurements in
Data Table 1.
5. Repeat step 4 on your partner.
6. Calculate the difference between your arm span and your height (arm span − height).
Record your calculations in Data Table 1.
7. Gather data from additional students in the classroom until you fill the data table.
Record the students’ name, gender and data in Data Table 1. You will have a total
of 25 individuals.
HYPOTHESIS #1
PREDICTION #1
________________________________________________________________
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DATA AND OBSERVATIONS
Data Table 1: Lab Partner Data
Arm span
Height
Difference
You
Partner
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Now that you have the data, we need to present it in a way that we can see
trends/relationships. We will use two types of graphs to “visualize” our data.
Graphically we will look at your data in two ways: A histogram and a scatter
plot.
Number of Purchases
A histogram measures the frequency of a data points over a range. For example if
you were a marketing person you’d want to know who was buying your product so
you know who to cater your advertising to. You might record the ages of everyone
who buys your product and create the histogram shown below.
Notice: The X axis represents data ranges. The data
has been broken into relevant “bins.” In other words
we count the number of individuals that fall into a
specific range (or bin). For example, we look at all
purchases intended for 1-5 year olds, together.
Scientists have to be careful to define their bins in
appropriate sizes to give their data the most
meaning.
According to this histogram, what is our target
demographic in terms of marketing our product?
Age for whom purchases were made (yrs)
A scatter plot looks at the relationship between two numbers. It looks to see if there
is a set proportion between two variables. For example, let’s say we want to know
whether people tend to marry people of the same age. To do this we can graph a
wife’s age against her husband’s age and look for a relationship. If there is one, we
should see a linear pattern in our graph. The slope of that linear line will give us the
average proportion of husband and wife’s age. If no relationship exists, the points
on our graph will be scattered with no recognizable pattern.
Notice:
There is a general linear trend, which tells us that
There is a positive correlation. As X increases so
does Y. This means:
The slope of this line (the proportion of a wife’s
age to her husband’s age) is close to 1. We can
therefore conclude that:
What about the dots that don’t fit on the line?
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Now you’ll graph your data both ways. Be sure to reference that graphing rules
sheet I gave you! In the histogram, you will be graphing the difference between
height and arm span.
Histogram Graph Title:
____________________________________________________________________
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The scatter plot will allow us to determine whether arm span and height are
correlated. Be sure to use the same units of measure on the X and Y axes.
Scatter Plot
Graph Title:
___________________________________________________________________
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Data Analysis Questions:
1. Did you accept the proportional statement as true? Why or why not?
2. Examine your histogram. Summarize the conclusions you can draw from
your data as shown on the histogram.
3. Examine your scatter plot. Summarize the conclusions you can draw from
your data as shown on the scatter plot.
4. Which type of graph presents your data in a more informative way? Explain.
5. For the sake of time and ease of experiment, we limited ourselves to a
population of teenagers. How might this have affected our data?
6. Identify the following components of the experiment:
a. Dependent Variable: ___________________________________
b. Independent Variable: _________________________________
c. Constant(s): ____________________________________________
d. Sample size: ____________________________________________
7. Was this a controlled experiment? Why or why not?
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Now that we have “held your hand” through the first activity, it is now time to cut you
loose and let you repeat this process in your lab journal. This is how we will be working
through lab activities this year. Your job, as a budding young science enthusiast will be to
keep and maintain a lab journal that documents your inquiry experiences in our class.
Human Proportions Lab Part II (put this in your lab notebook).
Please follow directions for how to set up your lab notebook that are written
on the page following this assignment.
Your problem: Some people have observed that the length of their foot is the same as the
length of their forearm. Others disagree saying there is no relationship between the two.
You have been assigned to investigate this phenomenon. Create a title, write a summary
of your activity, as well as a purpose for the lab. Label the space for the hypothesis,
which you will determine with your group. Leave space (a page) for your procedure,
create a data table for results (assume class data) , and answer the same questions
answered in part I, for part II (you must write out each question, then answer it). Set up
the graph axes for two graphs you will create (follow all graphing rules), and leave room
for your conclusions and suggestions for improvements. Don’t forget to update the index
when you finish.
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Bio Lab Journal Set up
Outside Cover – Write your Full name, period and teacher name in ink
Table of Contents: The first ten pages of your notebook will be your table of contents.
Copy the heading below on to the top of all ten pages.
Table of Contents
Date
completed
Lab/activity name:
Page #s
Poss. points
My grade:
As we complete labs we will write in the number and name of the lab (not just the number) and the
page numbers where the prelab assignment, hypothesis (where required), data gathered and
analysis and conclusions are required. Be sure to enter in the first few activities that we did (you can
call those activities instead of labes.
After setting up your journal Cut the remainder of this page off and tape it to the inside front of your
journal
----------------------------------------------------------------------------------------------------------------------------- ----Writing in lab journal – all writing should be done in pencil (this will change after this year).
Graphs must be on a page in the book. No loose pages or papers sticking out of the notebook.
Each lab:
Write the lab # and title across the top of a FRESH page. Do not start a new lab on the back of a
previous lab.
Pre-lab: To be done after reading the lab and is due the day of lab planning.
o In some cases I will assign specific questions to answer. In all other cases your prelab
will consist of
 a summary of what you are going to do in the lab
 the purpose of the lab
 Any questions the lab is asking you to answer before you begin the lab
 Additionally consider summarizing any relevant background that is new to
you. Remember your assessment will require you to know this info, so the
more you put into your journal, the more you will have to use.
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Planning and Procedure: Your group will work together to create a hypothesis and then
design an experimental procedure that will be implemented to test your hypothesis. Procedure
must be detailed and listed stepwise. Remember you will follow this procedure and therefore
the more detailed it is, the easier it will be for you. You are expected to revise this during the
experiment if there are issues.
Data: You will create tables/graphs to record all your data including observations,
measurements, or graphs of measurements. Graphs must be in your journal.
Conclusions: In the conclusion you should describe what your data says, using inferences
supported by data. At this point, you should check your prelab questions to be sure they are
answered correctly. Finally, within the conclusion discuss any problems with the procedures
and how they might improve.
Page numbering – pages should be numbered in the upper, outer corner of the page.
Table of contents: upon completing a lab journal entry, add the lab and appropriate pages to
your table of contents
Many of your labs will be graded through lab assessment (a quiz). You will have your lab
journal and be able to use what you produce for that lab only. Journals will also be collected
and graded. The quality of your journal entry should not change regardless of assessment
method. You may not know which method will be used to assess your lab.
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