A Special Assignment From NASA
Understanding Earth’s Atmosphere Through the
Integration of Science and Mathematics
by Justine E. Fox and Nicole J. Glen
ave your students ever wondered what
NASA scientists do? Have they asked you
what their science and mathematics lessons have to do with the real world? This
unit about Earth’s atmosphere can help to answer
both of those questions.
A Framework for K–12 Science Education (NRC
2012) explains that mathematical thinking is central to
science and therefore an essential practice of science
curricula. The National Science Education Standards
(NRC 1996) and Benchmarks for Science Literacy
(AAAS 1993) both suggest that mathematics and sci-
30
ence be linked via concepts and skills in each area.
The unit described here showcases “content specific
integration” of science and mathematics in that the
lessons meet content objectives from both science and
mathematics (Davison, Miller, and Metheny 1995).
The content objectives for mathematics from the new
Common Core State Standards for Mathematics are to
understand and reason about ratio concepts, including
converting measurements (6.RP), solving problems
involving area (6.G), and representing real-world problems graphically using one quadrant (5.G) (CCSSO and
NGA 2010). The content objectives for science are the
A Special Assignment From NASA
properties of Earth’s atmosphere and understanding
about science and technology (NRC 1996). Connections to the Framework for K–12 Science Education
include the following (NRC 2012):
Disciplinary core ideas
• Earth and space sciences—Earth materials and
systems (ESS2.A)
• Engineering, technology, and applications of science—Influence of engineering, technology, and
science on society and the natural world (ETS2.B)
Science practices
• Developing and using models
• Analyzing and interpreting data
• Using mathematics and computational thinking
• Constructing explanations
• Obtaining, evaluating, and communicating information
Crosscutting concepts
• Scale, proportion, and quantity
• Systems and system models
See Figure 1 for an overview of how elements of this
interdisciplinary unit address science, math, language arts, and social studies content.
Background
Prior to this unit, students had studied Earth science
topics related to processes on the Earth’s surface
(e.g., erosion and weathering, oceanography). After
this unit in science, students use knowledge they
gained about air pressure and the atmosphere to
learn more about various climates around the world.
In mathematics class, at the same time this unit was
taught in science, students learned and practiced twodimensional measurement and graphing, and thus
could apply these skills to the following unit at the
same time.
Students first learned the basic science content of
this integrated unit by investigating the answer to a
short mystery called “Here’s the Crusher,” from the
book Even More Everyday Science Mysteries (KonicekMoran 2010, p. 55–62). The mystery is about a boy,
Eric, who washes a water bottle under hot water, puts
the cap back on, and sets the water bottle on a surface
to dry. As Eric walks away from the water bottle, he
hears a crackling sound and notices that the water
bottle looks as if it had been crushed by something,
which leaves him wondering how this happened. This
“mystery” can be told to students as stated here in
order to engage them in this part of the unit if you do
not have access to this book.
After reading the mystery aloud together, students
discussed as a class what they thought happened to the
water bottle. After the discussion, students individually
created a question related to the mystery that they
would try to answer through an experiment with the
given materials, which were on a table in the back of
the classroom: empty plastic water bottles (such as
the kind that bottled water comes in), empty plastic
2-liter soda bottles, 12-quart tubs of ice water, and warm
water from the sink (the ideal water temperature is
110ºF, but this lab will work with tap water as cool as
75ºF). Most students asked questions such as “Why
did the water bottle collapse?” or “Why did the water
bottle shrink?” After students created their questions,
the teacher formed groups of three or four students
with similar questions, and each student in the group
formed an individual hypothesis to attempt to answer
the question about why the water bottle crushed.
Before students were allowed to investigate, they
completed the Materials and Procedure sections of
their Activity Worksheet and had it approved by the
teacher. This step kept the teacher informed about
what each group was testing and ensured that all group
members had reached a consensus about what they
wanted to test. It may be helpful to approve all of the
groups’ procedures before allowing anyone to begin
investigating so as to better manage the activity. For
safety and materials management, students were required to wear safety goggles and the teacher stayed at
the sink to supervise students’ use of the water to make
sure the surrounding area did not get wet or slippery.
Students first replicated exactly what Eric did in the
mystery and then were welcomed to use other available
materials and test different variables to observe other
outcomes. While investigating, students filled out the
Observations section of their Activity Worksheet and
recorded what they saw happen.
After the investigation, each group described
orally what it tested and what happened, answering
the group’s question and sharing any ideas with the
S e p t e m b e r 2 012
31
A Special Assignment From NASA
FIGURE 1
Unit outline
Science
Math
Building
background
knowledge
Doing air-pressure lab
NASA
assignment
Phase 1
Creating scaled map
of atmosphere layers
Calculating scales and
dimensions (areas
and perimeters) of
each layer
NASA
assignment
Phase 2
Analyzing map and
temperature graphs
Graphing temperature
vs. height of each
layer
NASA
assignment
Phase 3
• Researching in
science textbook for
information about
layers
Social studies
Writing letter to Eric for
conclusion of lab
• Deciding where
natural and
technological items
should be placed in
layers
class as to why group members thought their water
bottles shrunk. Most students said something about
air playing a role; some suggested that the air was
escaping. After students discussed the experiment,
the teacher explained while demonstrating with the
water bottle and water that when the water bottle is
rinsed with warm water, the air molecules inside the
water bottle expand and spread out. When the cap is
screwed back on and the bottle set aside, there is a
temperature difference between the warm air inside
the water bottle and the cooler air temperature surrounding it. As air inside the water bottle begins to
cool, the air molecules inside the water bottle cool,
as well, and get closer together, and therefore the
air takes up less space in the bottle. The water vapor
condenses and the water droplets take up less space
than the water vapor. As the air molecules get closer
together and the water vapor condenses, the pres-
32
English/
language arts
Researching online and
using other sources for
information about layers
Learning about natural
and technological
items, their geographic
locations on the Earth,
and their connections
to and importance in
human lives
sure inside the bottle becomes lower. The outside
air pressure pushes on the bottle, and since the air
and water vapor are taking up less room inside the
bottle, the stronger outside air pressure causes the
bottle to cave in. It may be helpful to draw a diagram
for students that represents this visually during the
teacher explanation.
As a formative assessment, students applied their
new knowledge by writing a letter to Eric explaining
what happened to his water bottle using the following
words: cold, condensing, warm, expanding, and molecules. This segment of the unit takes one to two class
periods to accomplish (about one hour total).
Becoming NASA scientists
After receiving this background information on air
pressure and understanding that air takes up space
(depending on your students’ prior knowledge of
A Special Assignment From NASA
these two concepts, more introductory lessons may
be needed), students were introduced to the special
assignment from NASA. Students were told that
NASA sent this special assignment because the organization needed their help. Together the class read
Phase 1 (see Activity Worksheet), and afterward the
murmur in the room suggested that students were
excited to begin this task. The teacher also briefly
explained Phases 2 and 3 so students knew the overall purpose of the assignment.
Phase 1
Phase 1 requires students to make a map of the atmosphere, but the map has to be scaled appropriately.
This is the first integration of mathematics content.
Making a scaled map helps students understand that
the real world often includes objects and distances
of greater measurements than can be presented
with human tools, so the objects and distances must
be scaled down and represented by a smaller measurement that is easier to work with. Together, the
teacher and students did the first two problems in
Phase 1 (see Activity Worksheet), which led to the
scale of 1 cm on students’ maps representing 20 km
in the atmosphere. After this was established, students needed to figure out how many centimeters on
their map each layer of the atmosphere should be.
Once all of the groups had the new measurements
established for each layer of the atmosphere, and
these were checked by the teacher, students started
drawing their maps. They were provided with poster
paper already cut to 76 cm tall by 61 cm wide. The
paper was precut to these measurements to allow
the math and scaling of the maps to work out evenly
using numbers predetermined by the teacher.
Some of the difficulties students might encounter
during Phase 1 include trouble measuring, measuring from the incorrect place, forgetting a layer of the
atmosphere, or miscounting while measuring the
scale and thereby skewing the entire map. It is a good
idea to have students draw their maps in pencil first
and then trace over them with a marker to eliminate
too many groups redrawing their maps. When all of
the groups finished coloring and labeling their map
measurements, they found the area and perimeter of
each atmosphere layer in order to conceptualize the
scaled size of each of the layers compared to each
other and use this as evidence during Phase 3 to
determine where naturally occurring and technological items might be situated within the atmosphere or
across the different regions of the atmosphere. This
also directly connected to what students were learning in mathematics during
this time: two-dimensional
measurement. It may also
be helpful to make it clear
and model for students
that they need to show
their mathematical work
in order to receive credit
on Phase 1. For example,
point out where they
can find the measurements of each layer
and how work was
shown for the
S e p t e m b e r 2 012
33
A Special Assignment From NASA
FIGURE 2
Student maps
problems the class did together at the beginning of
the phase. Phase 1 may take up to three class periods
for most groups.
Phase 2
Together the class read Phase 2 (see Activity Worksheet), which requires students to overlay a temperature-versus-height graph of the atmosphere onto
their scaled maps from Phase 1. To begin, show students how to make and label axes on their maps and
space the tick marks apart, and allow them to do the
34
same on their group’s map. Next, model for students
and talk together about how to place information on
the graph from the first couple of problems in the
Phase 2 table (see Activity Worksheet). Demonstrate
and explain the placement of the problems on your
own example, and have students complete the same
on their group’s map. Modeling and completing the
first couple of problems together may help eliminate
the amount of individual attention and direction you
will need to give each group. The final step of Phase
2 is to analyze the data that are now graphed on the
maps. To help students analyze their maps, a class
A Special Assignment From NASA
discussion was held first and guided by
the following questions:
FIGURE 3
• What would your graph look like if the
temperature was increasing steadily
with height?
Name:____________________________
• What would your graph look like if the
temperature was decreasing steadily
with height?
• What would your graph look like if
the temperature varied with height?
Rubric
Completed Phase 1 narrative (10 pts.)
• Found the correct perimeter and area of
each layer
Completed Phase 2 narrative (10 pts.)
• Which of these scenarios is actually
shown on your graph? How do you
know?
• Answered question 4 correctly in a sentence
• What does your graph show about
how temperature changes as you go
higher in the atmosphere?
• Provided three facts about each layer in the
atmosphere
Phase 2 directly connected to what
students had lear ned earlier in the
school year in mathematics: plotting
coordinates on a grid with x- and y-axes
and collecting, graphing, and analyzing
data. This phase may take up to two
class periods for most groups, but once
they are finished, students are ready to
problem solve like scientists.
Completed Phase 1 atmosphere map (10 pts.)
Phase 3
Phase 3 of the NASA special assignment requires students to figure out
which layer of the atmosphere NASA
should allow certain technology, such
as airplanes, space shuttles, satellites,
and radio signals, to travel through and
to. To help with this determination, students also had to research some additional information about each phase of
the atmosphere. For example, students’
research about the thermosphere led
them to learn that this is also where
the ionosphere is located and that it is
a layer made of charged particles that
allows radio waves to travel through the
atmosphere. Students completed this
research with their science textbooks,
but additional resources can be found
______
• Made correct calculations
Completed Phase 3 narrative (10 pts.)
______
______
______
• Made accurate measurements on the map
• Shaded each layer differently
• Labeled all layers
• Labeled the kilometers on the map where each
layer begins and ends
Completed Phase 2 atmosphere map (10 pts.)
______
• Graphed the horizontal and vertical axes correctly
• Graphed the data onto the map accurately
Completed Phase 3 atmosphere map (10 pts.)
______
• Placed the pictures of the objects in the correct
layers of the atmosphere
• Wrote a fact about each layer on the map or on
paper attached to the map
Group participation (30 pts.)
______
• Contributed actively to the group project
• Worked well with all group members
Completed the assignment in a timely manner (10 pts.)
______
• Completed and handed in map and narratives by
the deadline given for completing the assignment
Total: _______
S e p t e m b e r 2 012
35
A Special Assignment From NASA
online (see Resources). Each student in the group
was responsible for researching a layer of the atmosphere and then sharing that research with the rest
of the group; students were also allowed to work together once they had finished their own layer or if
they needed help. Once the entire group had at least
two to three facts on each layer, the group wrote
summaries of these facts directly on its map or on index cards that the group attached to the sides of the
map. Next, in order to model what students would
do with the technological items, together the class
determined where some naturally occurring items,
such as mountains, clouds, auroras, and a meteor,
would be placed in the atmosphere. Then students
were provided with pictures of technological items
(see Resources) that NASA needed help determining where to place. The pictures also contained
some basic facts about each object to help students
make their decisions. Students used their maps,
atmosphere facts, and textbooks to explain where
they thought the object should travel to or through
and why they thought so. Students glued the objects
on their maps and presented orally their claims and
reasons why they placed the objects where they did
(Figure 2). Phase 3 connected more to scientific inquiry skills, but students used mathematics to read
the information on their maps and graphs and as reasons for their placement of the objects. Phase 3 may
take up to two class periods to accomplish.
Conclusion
A rubric was used to assess students on their calculations, maps, graphs, placement of technological objects, and reasons for placing the objects where they
did (Figure 3). Throughout this unit, students were
eager to participate, as each day presented a unique
task that used their science and mathematics knowledge. Students always knew their purpose and goal,
which led to superb group communication and col-
Justine E. Fox ([email protected])
is a sixth-grade Earth science teacher at Qualters
Middle School in Mansfield, Massachusetts.
Nicole J. Glen ([email protected]) is an assistant
professor in the Department of Elementary and
Early Childhood Education at Bridgewater State
University in Bridgewater, Massachusetts.
36
laboration. All students felt accomplished when looking at their group’s final product. The integration of
science and mathematics in a unit that challenged
their problem-solving and inquiry skills led students
to make connections with real-world situations and
understand the importance of what they were learning in both subjects. n
Acknowledgments
Thank you to Mr. Steven Alves and his 2011 sixth-grade
math/science class at the Edgar B. Davis K–8 School in
Brockton, Massachusetts, for participating in this unit.
References
American Association for the Advancement of Science
(AAAS). 1993. Benchmarks for science literacy. New
York: Oxford University Press.
Council of Chief State School Officers (CCSSO) and the
National Governors Association (NGA). Common core
state standards for mathematics. www.corestandards.
org/assets/CCSSI_Math%20Standards.pdf.
Davison, D.M., K.W. Miller, and D.L. Metheny. 1995.
What does integration of science and mathematics
really mean? School Science and Mathematics 95 (5):
226–30.
Konicek-Moran, R. 2010. Even more everyday science
mysteries: Stories for inquiry-based science teaching.
Arlington, VA: NSTA Press.
National Research Council (NRC). 1996. National science education standards. Washington, DC: National
Academies Press.
National Research Council (NRC). 2012. A framework
for K–12 science education: Practices, crosscutting
concepts, and core ideas. Washington, DC: National
Academies Press.
Resources
Geology & geography for kids—www.kidsgeo.com
Windows to the universe (to find photos of technological
items)—www.windows2universe.org
YouTube videos demonstrating air-pressure lab
Joy physics: exp #16 bottle crush—www.youtube.com/
watch?v=pHuvqqf6Qug
Water bottle about to implode due to delta pressure—
www.youtube.com/watch?v=JV1FocnTkAc
A Special Assignment From NASA
Activity Worksheet: Becoming NASA Scientists (continued)
Name: _____________________________________
Background
Question
___________________________________________________________________________________________
___________________________________________________________________________________________
_________________________
Hypothesis: I think that…
___________________________________________________________________________________________
___________________________________________________________________________________________
_________________________________
Materials
___________________________________________________________________________________________
___________________________________________________________________________________________
_________________________________
Procedure
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
Observations
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
Conclusion
Dear Eric,
Your water bottle crushed because
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
S e p t e m b e r 2 012
37
A Special Assignment From NASA
Activity Worksheet: Becoming NASA Scientists (continued)
Phase 1
Dear students,
We scientists at the NASA (National Aeronautics
and Space Administration) headquarters in Washington, DC, need your help! We lost all of our maps
of Earth’s atmosphere and need you to help us create a new map of Earth’s atmosphere showing all of
the layers and the temperature differences in each
layer.
The map should be about 76 cm tall and about 61 cm
wide.
1. The first 4 cm of the map should represent the
Earth, with the rest of the 72 cm left for the atmosphere. Draw in the Earth, shade it green, and
label it Earth.
2. The 72 cm that are left on the map should show
the layers of the atmosphere up to about 570 km,
the last layer being the exosphere. Therefore, you
have 72 cm to represent 570 km, so each inch on
your map should represent how many km?
1 cm (on the map) = __________km
3. Now you know how many kilometers are represented by 1 cm on the map. The first layer above
the Earth to record is the troposphere, which
exists in the first 10 km of the Earth. Shade in the
troposphere on your map using a light-blue color
and label this layer troposphere. (Reminder: 1 cm
= _____ km, therefore how many centimeters do
you need above the Earth to represent 10 km?)
_____ cm = 10 km
4. Now that you have the troposphere colored in,
shade in the next layer with a darker blue and
label it as the stratosphere. The stratosphere exists between 10 km and 50 km above the Earth,
therefore it makes up the next 40 km above the
38
troposphere. How many centimeters above the
troposphere represent the stratosphere?
_____ cm = 40 km
5. The troposphere and the stratosphere have now
been shaded in. The next layer should be shaded
an even-darker-colored blue and labeled the mesosphere. The mesosphere exists from 50 km to
85 km above the Earth’s surface, meaning that it
makes up the next 35 km of the atmosphere. How
many centimeters above the stratosphere are to
be shaded in as the mesosphere?
_____ cm = 35 km
6. The thermosphere is the greatest layer in Earth’s
atmosphere. Label the next section as the thermosphere and shade this layer in with a darker
blue (you can begin to mix the blues with gray/
black to make it even darker). This layer exists
from 85 km above Earth’s surface to about 500
km above Earth’s surface. Shade in this region
up to 415 km above the mesosphere.
_____ cm = 415 km
7.
The exosphere is the last layer of the atmosphere
before outer space. This layer should be shaded
in almost a light-black or gray color and labeled
as the exosphere. This layer exists from 500 km
above Earth’s surface to outer space, so it should
take up the rest of the map.
A Special Assignment From NASA
Activity Worksheet: Becoming NASA Scientists (continued)
Good job! You have almost completed Phase 1 of your special assignment. Double-check and make sure you have
done the following:
• Labeled each layer
• Shaded in each layer
• Included in kilometers where each layer begins on the far-left-hand side of the map (for example, the boundary
between the troposphere and stratosphere should be labeled as 10 km on the far left of your map)
Now we need to plug important information from your map into our computer system. Make sure you show all of
your work for the following questions.
8. What is the perimeter of your map in centimeters?
9. What is the area of your map in square centimeters?
10. What is the perimeter of the troposphere on your map in centimeters?
11. What is the area of the troposphere on your map in square centimeters?
12. What is the perimeter of the stratosphere on your map in centimeters?
13. What is the area of the stratosphere on your map in square centimeters?
14. What is the perimeter of the mesosphere on your map in centimeters?
15. What is the area of the mesosphere on your map in square centimeters?
16. What is the perimeter of the thermosphere on your map in centimeters?
17. What is the area of the thermosphere on your map in square centimeters?
S e p t e m b e r 2 012
39
A Special Assignment From NASA
Activity Worksheet: Becoming NASA Scientists (continued)
Phase 2
Congratulations on your completion of Phase 1 of the special assignment! Earth’s atmosphere has been drawn to
scale on your map, you have labeled each layer with its name and kilometers above Earth’s surface, and you have
given us all of the layer (besides the exosphere) perimeters and areas on your map. This next part of your special
assignment is to show us the temperature differences throughout Earth’s atmosphere.
Here is a table with temperature changing with altitude (height):
Temperature (C)
Height (km)
20
0
–55
10
–55
20
0
50
0
55
–85
85
–90
90
–80
100
700
140
Given these values for temperature changes in the atmosphere with height, we need you to plot this information on
your map.
1. Turn your map into a graph. Horizontally at the bottom of your map make a scale for the temperature. Start
in the left-hand corner at –200°C and make tick marks counting up by 50s all the way to 700°C. (Hint: There
should be 18 tick marks in total starting from –200 in the bottom left corner, –150 next to it, -100, and so on
until you get to 700 in the right-hand corner.)
2. Now that you have the horizontal axis made for temperature, make a vertical axis for height in kilometers. You
already have the kilometers marked at each layer in the atmosphere, so fill in tick marks counting up by 10s all
the way up to 570 km. (Hint: Remember what 1 cm equals in kilometers on the map, and keep the tick marks
evenly spaced.)
3. Graph the information from the table above using a bright marker and connect all of the dots. Label this line as
Temperature Changes in the Atmosphere.
4. What do you notice about this line? Is temperature increasing steadily or decreasing, or does it vary with
height?
40
A Special Assignment From NASA
Activity Worksheet: Becoming NASA Scientists (continued)
Phase 3
We suspect that the map you are making for us is
almost complete! Well done, middle school scientists!
You are now about to enter Phase 3 of your special
assignment, the last and final stage.
You have all of the layers mapped out for us, along
with the temperature changes, but we need you to
include facts about each layer of the atmosphere
on your map. This will help you determine where we
should send our specialized technological equipment.
1. First, find at least three facts to write about each
layer. List your three facts for each layer below.
Use your textbook to help you find information:
2. With your group, select one to three facts about
each layer to write on your map. Write the facts
for each layer inside each layer’s shaded region
using a dark marker.
3. Each group will now receive a picture of an
airplane, a rocket ship, a meteor, a satellite, radio
signals, clouds, and a mountain that you must
place in what your group sees as the best-fit layer
for that object to be in. You may use information
from your science textbook as well as the facts
and data on your map as evidence and reasoning for why these objects should be placed in
the layer you chose. Be prepared to share your
answers with the rest of the class.
Troposphere
i.
ii.
iii.
Stratosphere
i.
ii.
iii.
Mesosphere
i.
ii.
iii.
Thermosphere:
i.
ii.
iii.
Exosphere
i.
ii.
iii.
S e p t e m b e r 2 012
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