Unit 4
The Science of Paper Folding
In order to “see” the figure that is created by paper folding, another method of
constructing the figure needs to be explored. Making the Dragon is a hands-on
activity that enables students to build a figure using rotational symmetry. The
similarity of the parts to the previous step is evident as the students assemble the
Dragon “curve.” The activities in this unit are designed to be completed in
cooperative groups of two or four students.
Scientific Method
The Scientific Method is a systematic approach to problem used by scientists in all
fields of study. Typically, it involves a series of steps that guide the scientist in
testing hypothesis. After recognizing a problem, a scientist attempts to form a
hypothesis or prediction that can be tested. A controlled experiment is conducted in
which one factor or variable is changed and others are held constant. Observations
and data are recorded and analyzed to allow the scientist to draw conclusions about
the original question and their hypothesis.
Interestingly, this basic skill of scientist is difficult for students to master. Guided
practice of the students through the experiments of this unit allows them to develop
the habits of good scientists. Manipulation of a single variable in each scenario
encourages students to gain understanding and procedural competency as they answer
the question, “How many times can a paper strip be folded in half?” Thus, this unit
allow the basics of Paper Folding” to be used as a tool to teach the steps of the
Scientific Method.
Lab: Paper Folding I
S
SS
Sunshine State
Standards
SC.A.1.3.1
SC.A.1.3.5
SC.H.1.3.1
SC.H.1.3.4
SC.H.1.3.5
SC.H.1.3.7
SC.H.2.3.1
Lessons in Paperfolding
Grade Level:
2-8
Materials:
1” x 11” strips of paper (enough for 3 per student)
Procedure:
1. Introduce the steps of the Scientific Method.
I. State the Problem (recognize what you want to study; ask a question)
II. Form a Hypothesis (make a prediction about the problem that can be tested)
II. Test a Hypothesis (conduct a “controlled experiment” in which one factor is
manipulated to see its affect on another variable and all other factors are
controlled or held “constant” by the experimenter.)
A. Plan (develop the steps of the experiment)
B. Conduct the experiment (follow the procedure ‘to the letter’)
C. Collect and record data (measurements, diagrams, data tables, etc.)
IV. Analyze the data (perform calculations, make graphs, and otherwise organize
data)
V. Draw conclusions (make statement about the hypothesis based on the results
of the experiment - do the results support/reject the hypotheses?)
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2. Pose the following question to the students: “How many times can a piece of
paper be folded in half?”
3. Lead the students in making predictions or educated guesses to answer the
problem (i.e., experience tells them that 100 folds are unlikely, but that the paper
definitely can be folded more than once). Explain to the students that educated
guesses are “hypotheses.”
4. Ask the students how they could test their hypothesis - to prove them right or
wrong. Lead the students to development of a procedure that will lead to reliable
results.
Possible procedure:
1. Fold a strip of paper in half (lengthwise).
2. Continue folding the paper i half (always in the same direction) until the
paper cannot be folded again.
3. Record the number of times the paper folded.
4. Complete two mor “trials” (fold two additional strips), record the number
of folds for each and find the average number of folds for the three trials.
Conclusion:
Each student will be responsible for developing a lab conclusion that answers the lab
question, “How many times can a piece of paper be folded in half?” Using the
information gathered during the experiment (i.e., average number of folds), each
student will evaluate his/her hypothesis and give reasoning behind accepting or
dismissing it.
Discussion:
Discuss the following:
Explanations behind the original hypotheses
Limiting factors for the number of folds possible (paper thickness, size, etc.)
What experiments could be conducted to test these limiting factors?
Lab: Paper Folding II - Variation: Kind of Paper
S
SS
Sunshine State
Standards
SC.A.1.3.1
SC.A.1.3.5
SC.H.1.3.1
SC.H.1.3.4
SC.H.1.3.5
SC.H.1.3.7
SC.H.2.3.1
Lessons in Paperfolding
Grade Level:
2-8
Materials:
1” x 11” strips of different kinds of paper (i.e., construction paper,
tissue paper, notebook paper)
Procedure:
1. Ask the question, “Does the kind of paper used affect the number of times it can
be folded?”
2.
After students develop hypotheses, introduce the concepts of “variable” and
“control.” Discuss the importance of having only one variable (the kind of paper)
in accurately determining the effect of paper type on the results.
* A variable is a factor that changes in an experiment.
*A control is a factor that is kept constant for all trials of an experiment.
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3. Allow students to work collaboratively in pairs to develop a procedure that tests
the hypothesis.
Possible procedure:
1. Fold a strip of paper in half (lengthwise).
2. Continue folding the paper in half (always in the same direction) until
the paper cannot be folded again.
3. Record the number of times the paper folded.
4. Repeat the procedure for two more paper strips of different kinds of
paper. Be sure to record the kind of paper and number of folds for each
on a data table.
4. Instruct the students to have the teacher approve their procedure before
beginning the experiment. Once the teacher verifies the appropriateness of the
lab procedure, the teacher will provide students with the necessary materials to
carry out the experiment.
5. The student pairs will complete the experiment and record the necessary data.
Conclusion:
Each pair of students will be responsible for developing a lab conclusion that answers
the lab question, “Does the kind of paper used affect the number of times it can be
folded?” Using the information gathered during the experiment (i.e., the number of
folds for each kind of paper), each pair will evaluate their hypotheses and give
reasoning behind accepting or dismissing it.
Discussion:
Discuss the following:
What was the variable in this experiment?
What things were controlled?
How did your predictions differ from your results?
What other factors or variables, if any, can change the outcome of the
experiment?
Summarize the results by discussing how changes in the variable affect the final
results.
Lab: Paper Folding III - Variation: Size of Paper
S
SS
Sunshine State
Standards
SC.A.1.3.1
SC.H.1.3.1
SC.H.1.3.2
SC.H.1.3.4
SC.H.1.3.5
SC.H.1.3.7
SC.H.2.3.1
SC.H.3.3.4
Lessons in Paperfolding
Grade Level:
2-8
Materials:
Strips of paper that vary in length
Procedure:
1. Ask the question, “Does the size of the paper used affect the number of times it
can be folded?”
2. Instruct students to work in pairs to develop hypotheses and procedures that
allow them to record the dimensions of the paper strips during data collection.
Also, remind students of the importance of a single variable which is the size (not
the kind or thickness) of paper used.
3.
Allow students to conduct their experiments, being sure to follow their directions
carefully.
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Possible procedure:
1. Cut several different sizes of paper strips.
2. Use a ruler to measure the length and width of each strip. Record the
measurements.
3. Fold each strip i half (lengthwise) until it cannot be folded again.
4. Record the number of folds for each of the strips in a data table along
with the dimensions (length and width) of each strip.
Conclusion:
Each pair of students will be responsible for developing a lab conclusion that answers
the lab question, “Does the length of paper used affect the number of times it can be
folded?” Using the information gathered during the experiment (i.e., the number of
folds for each size of paper), each pair will evaluate their hypotheses and give
reasoning behind accepting or dismissing it.
Discussion:
Discuss the following:
Importance of single variables in controlled experiments
Importance of following procedures and recording data accurately
What is the trend that the experiment results illustrate? (i.e., when the size
changes...)
Which has the greater impact —size or kind of paper?
Would the way the paper was folded affect the results?
How could the manner of folding be tested? (develop another experiment)
Lab: DNA Base Complementarity
DNA, deoxyribonucleic acid, is the hereditary material that is passed on from one
generation to the next during reproduction. It is what genes and chromosomes are
made of. DNA also directs and controls the development and activities of all the cells
in an organism. One would imagine that the diversity of structures and functions of
cells and organisms would require a complex coding system, but DNA actually has
only FOUR different building codes. Much like the 26 letters of the alphabet, they
can be arranged to make many different messages!
DNA itself is actually a simple molecule. Each DNA molecule consists of two long
strands of smaller units called nucleotides. The nucleotides are made of a sugar
molecule and a phosphate molecule bound to one of four nitrogenous bases: thymine
(T), adenine (A), cytosine (C), or guanine (G). DNA is always found as a double chain
of one sequence of nucleotides paired with another sequence of nucleotides.
The structure of the DNA molecule is often compared to that of a ladder that has
been twisted. The sugar and phosphate groups alternate continuously the whole
length of the molecule and form the “uprights” of the ladder. The “rungs” of the
ladder are occupied by pairs of DNA bases. The shape and chemical makeup of the
bases are such that they bond in a predictable manner: cytosine always pairs with
guanine and adenine always pairs with thymine.
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This double helix structure of DNA was discovered in 1953 by James Watson and
Francis Crick (with help from Linus Pauling and Erwin Chargaff, among others). They
found that the complementary nature of the base pairing could explain how each
strand of DNA could be used as a template for the replication of a new strand.
Grade Level:
5-8
Materials::
1” x 11” strips of paper ( enough for three per student)
Procedure:
1. Place a Step 3 paper strip on the desk with the marked edge (“X”) on the left as
illustrated. Write an “M” at the opposite end of the paper strip.
X
M
2.
X
L
L
3.
X
Write the L-R code for each turn on the crease for Step 3, using the “traveling”
method or notating peaks as R and valleys as L.
L
R
L
L
R
M
R
Rip Step 3 in half along the midpoint (center) fold, eliminating the center “L”
fold.
L
R
<- tear ->
L
4.
R
M
R
Use the following rules to correlate DNA bases to the L-R sequences in the paper
strip.
A. Code the bases starting at the endpoints X and M and work towards the tear
(former midpoint).
code
X
L
L
R
code
L
Lessons in Paperfolding
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R
M
R
Unit 2
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B.
Assign the DNA bases according to the following fold sequences (note:
there must be a paired sequence to assign a base).
LL = A
RR = T
LR = C
RL = G
code
X
L
L
R
code
L
C
A
R
G
C.
M
R
T
Write A, T, C, or G in each space BETWEEN two creases of the step four
paper strip as shown here for Step 3.
code
X
L
A
L
C
R
code
L
5.
G
R
T
M
R
Fill in the table below with the Step 3 L-R and DNA base sequences for the X
and M segments. Then repeat the L-R and DNA coding on the Step 4 paper strip
and predict the Step 5 sequence.
“X” segment
“M” segment
Step 3: L-R sequence
Step 3: DNA sequence
Step 4: L-R sequence
Step 4: DNA sequence
Step 5: L-R sequence
Step 5: DNA sequence
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DNA Complementarity and Paper Folding
Activity Sheet
1. Complete the table for both the L-R coding sequence and the DNA coding sequesnce.
“X” segment
“M” segment
Step 3: L-R sequence
Step 3: DNA sequence
Step 4: L-R sequence
Step 4: DNA sequence
Step 5: L-R sequence
Step 5: DNA sequence
2. What do you notice about the base sequence pattern WITHIN each step?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
3. Why/how is this pattern formed?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
4. What patterns develop BETWEEN the steps?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
5. Predict the L-R sequence for Step 6.
_________________________________________________________________________________
6. What are L-R sequences for the”X” and “M” segments of Step 6?
X
M
7. What are DNA sequences for the “X” and “M” segments of Step 6?
X
M
8. Bonus: Color the spaces between the folds on the Step 3 and Step 4 paper strips with “complementary”
colors according to the DNA bases they re[present and using the color key below:
A = red
T = green
G= orange
C = blue
Question: What pattern can be seen when the strips are colored?
_________________________________________________________________________________
_________________________________________________________________________________
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Activity Sheet Answers for
Lessons in Paper Folding Unit 4
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DNA Complementarity and Paper Folding
Activity Sheet Answers
“X” segment
“M” segment
Step 3: L-R sequence
LLR
LRR
Step 3: DNA sequence
AC
GT
Step 4: L-R sequence
LLRLLRR
LLRRLRR
Step 4: DNA sequence
ACGACT
AGTCGT
Step 5: L-R sequence
LLRLLRRLLLRRLRR
LLRLLRRRLLRRLRR
Step 5: DNA sequence
ACGACTGAACTGCT
AGCAGTTCAGTCGT
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Blackline Masters for
Lessons in Paper Folding Unit 4
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Lessons in Paperfolding
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DNA Complementarity and Paper Folding
Activity Sheet
1. Complete the table for both the L-R coding sequence and the DNA coding sequesnce.
“X” segment
“M” segment
Step 3: L-R sequence
Step 3: DNA sequence
Step 4: L-R sequence
Step 4: DNA sequence
Step 5: L-R sequence
Step 5: DNA sequence
2. What do you notice about the base sequence pattern WITHIN each step?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
3. Why/how is this pattern formed?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
4. What patterns develop BETWEEN the steps?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
5. Predict the L-R sequence for Step 6.
_________________________________________________________________________________
6. What are L-R sequences for the”X” and “M” segments of Step 6?
X
M
7. What are DNA sequences for the “X” and “M” segments of Step 6?
X
M
8. Bonus: Color the spaces between the folds on the Step 3 and Step 4 paper strips with “complementary”
colors according to the DNA bases they re[present and using the color key below:
A = red
T = green
G= orange
C = blue
Question: What pattern can be seen when the strips are colored?
_________________________________________________________________________________
_________________________________________________________________________________
Lessons in Paperfolding
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