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Get The Picture!
Overview
This lesson was written in accordance with the National Teacher Training
Institute (NTTI) format, which focuses on the utilization of instructional
television in the classroom.
The activities found in this lesson provide students with a hands-on
experience which will simulate the process of downloading actual data from a
High-Energy Satellite, and allow students to translate these data into colored
or shaded pixels.
Length of Lesson
Instructional Video/Technology
- Star Finder #2 Pictures from Data. TI-82 Graphics Calculator, Imagine the
Universe! (High-Energy Astrophysics Learning Center) CD or Website:
http://imagine.gsfc.nasa.gov
Learning Objectives
- Students will be able to (a) simulate data transfer from a gamma-ray
satellite to a computer, and (b) create an image from these data.
- Students will use matrix addition or subtraction to operate on
data collected by a gamma-ray detector.
- Students will be able to locate discrete gamma-ray sources in the
Universe by using the scientific method.
Prerequisites
- Students should have a basic understanding of matrix addition and
subtraction.
- Students should have a basic understanding of the
electromagnetic spectrum and
concepts in astronomy/space science. See Imagine the Universe! (High-Energy
Astrophysics Learning Center) CD or Website: http://imagine.gsfc.nasa.gov for
more information.
National/Regional Standards Correlations
- Virginia Mathematics Standards of Learning: A-4
- Virginia Science Standards of Learning: 6.2, 6.10, LS.1, PS.1
- Virginia Computer/Technology Standards of Learning: C/T8.1
- NSES Content Standards (5-8 and 9-12) A: Science as Inquiry; D:
Earth and Space Science; E: Science and Technology, and G: History and
Nature of Science
- NCTM Standards (5-8) Standard 9: Algebra; Standard 10:
Statistics. NCTM Standards (9-12) Standard 5: Algebra, Standard 10:
Statistics, Standard 12: Discrete Mathematics
Materials
* each egg crate holds 30 eggs. You can get these from most any restaurant.
Previewing Activities
What are
gamma-rays and what can they tell us about the cosmos?
Gamma-rays are the most energetic form of
electromagnetic
radiation, with over 10,000 times
more energy than visible light photons. If you could see gamma-rays, the night
sky would look strange and unfamiliar. The familiar sights of constantly
shining stars and galaxies would be replaced by something ever-changing.
Your gamma-ray vision would peer into the hearts of solar flares,
supernovae,
neutron stars,
black holes,
and
active galaxies
. Gamma-ray astronomy presents unique
opportunities to explore these exotic objects. By exploring the Universe at
these high energies, scientists can search for new physics, testing
theories and
performing experiments which are not possible in Earth-bound laboratories.
Most gamma-rays are absorbed by the Earth's atmosphere. Thus, cosmic
gamma-rays are typically observed from high-altitude balloons and satellites.
As scientists seek to maximize the amount of useful data per observation
dollar
spent, they often will sum many smaller exposures to make a longer exposure
which can reveal the source in greater detail. Exposure is a measure of how
much useful data is obtained from any given observation.
In gamma-ray astronomy, exposure is even more crucial than usual. Typically,
as you go up in energy, any individual source emits fewer photons. Since
gamma-rays are the highest energy photons, they are the most precious. Many
gamma-ray observations of even the strongest sources can be weeks in
duration.
In order to simplify these concepts, the first activity will
demonstrate how
the number of counts are assigned to a pixel or a predetermined location
on the
detector. The second activity demonstrates how the data are converted into
colors or shades which allow us to view an image of a cosmic source.
In the first exercise, the pennies will represent the photons,
and the egg
crate separators represent the receiving instrument on the satellite. Let
students take turns tossing a few pennies at a time into the egg crate
separator. Continue until all 100 pennies have been tossed. If some do not
land in the crate, do not worry, not all photons hit the high-energy
satellite.
Count the number of pennies (photons) in each cup and fill in the
corresponding
6X5 grid.
Note: There are six vertical and five horizontal cups.
Samples of Penny Toss and Corresponding Matrix
The second activity simulates the concept of binning. This is very
similar to what you do with a histogram when you use a range of numbers
for each
category. You may assign the following colors to the data in the penny toss
0-3 = black; 4-8 = dark gray; 9-13 = light gray; numbers >14 = white.
If your
numbers do not correspond to the ranges we suggest, modify the ranges. Use
the values you put into your 6X5 grid in the first activity to color in a
a new 6x5 grid. The picture below shows our data once colors have been
filled in. In our experiment, 91 pennies landed in the egg crate and 9 on
the floor.
Focus For Viewing
Say: Now that we have simulated the collection of photons and turned numbers
into images, let's see how more complicated images are made from
numbers. Raise
your hand when you hear the explanation of a pixel.
Viewing Activity
- Star Finder #2; Pictures from Data. Use the MEMORY feature of your
VCR and
set the memory at the section of Science Links where you see the gray scale
picture of a grid. You will later use the memory function to cue to this
section. REWIND the video to the Science Links Logo. PLAY: You will
see two
kids on skateboards. The hostess says "Let's make a video." PAUSE after the
hostess says "These minute video puzzle pieces are electronic impulses called
picture elements or pixels." Students should have hands raised and
respond with 'pixel' means "picture element."
- FOCUS: Ask students to brainstorm examples of where they find images made
up of pixels. Some examples might include: on the television, on a computer
screen, pictures taken by a digital camera, at football games when a lot of
people hold up small signs to make a large image, on the scoreboard of
Camden Yards, etc. Say: Let's see
what example the video shows us, and then I want you to tell me what we call
pictures created from numbers (digital pixels). RESUME. STOP when the
hostess
says "The pictures that the Hubble Space Telescope is sending are
pictures from
numbers, too", and you see the picture of the Hubble Space Telescope.
Use the
MEMORY function to fast forward to the section where you see the black
and white
grid.
- FOCUS: Say: Most pictures are made of different colors, or shades of
colors. Let's see how a computer determines brightness, darkness, or which
color to use. PLAY. STOP after the hostess says, "In this case, it's the
number of different shades between white and black that can be stored in one
byte." Use the MEMORY function to rewind to the beginning of the gray scale
grid.
- FOCUS: Say: This time I want you to concentrate on how the numbers are
assigned a color or shade so that when I stop the video, you will be able to
explain the process. RESUME. Again, STOP after the hostess says, "In this
case, it's the number of different shades between white and black that
can be stored in one byte."
Post Viewing Activities
Activity 1: Simulation of Data Collection
You will need to mark each egg crate separator in such a manner that you
can identify each cell. Labels are available in the Materials List which
can be printed and taped to the top and side of each egg crate separator.
Prepare each egg crate by taping the labels A-E along the top and 1-6 along
the side so that each egg cup can be uniquely identified.
Tell students that since we understand how numbers are assigned to
different shades or colors, we can examine how scientists use high-energy
data to determine the location of a source emitting gamma-rays. The
activity we are about to do simulates a high-energy satellite (such as the
Compton
Gamma-Ray Observatory) collecting data over time. Each group will
be given one day's collection of high-energy photons, which they will enter
into a 6 X 5 matrix.
Divide students into five groups (A-E). There is one egg crate separator
needed per group. Stack the five egg crate separators on top of each other
and place them on the floor at the edge of a table. Have a student or the
teacher drop 20 pennies into the top layer of the egg crate separators,
making sure the pennies are dropped from roughly the same location each
time. This simulates a discrete source in the sky. The pennies should fall
into several of the cups. Remove the top layer and hand it to Group A.
Repeat the process of dropping 20 pennies from roughly the same location
into each layer of egg crate separators, and giving one layer to each
group.
Once each group has an egg crate separator with pennies in the cells, you
will use matrix addition to sum the data. Students can enter their 6X5
matrix in the TI-82 graphing calculator
, making sure the letter of the
matrix matches the letter of each group. Remind the students that if a
cell is empty they will enter 0 in that location. Students can then link
and copy the data from the other calculators so that they have five
matrices (A-E) to add, or they can copy their matrix on an overhead
transparency and sum the data in the matrices by hand.
Tell the students that the location of a high-energy source cannot be
determined unless the source's data shows statistical significance. In
order to determine statistical significance, follow the procedure and
explanations in "Finding a Source".
ACTIVITY 2: Using Real Data
Now the students will be taking on the role of a high-energy astronomer in
order to determine the minimum number of days of data needed to find the
source. The importance of this real life activity becomes obvious when one
learns of the cost associated with collecting this data. Hundreds of
thousands of dollars are spent each day collecting data, so finding a
source in the least amount of time is imperative to astronomers.
Hand students the CGRO Data Collected Over 4
Hours and have them predict
where any source(s) is(are) located. This allows for a good discussion of how
to label the matrix so that all the students will know which cell is being
discussed. Then have them look at CGRO Data
Collected Over 1 Day to see if their predictions may still be correct
or if they change their minds about where any source may be located.
Using the CGRO Data Collected Over 1
Day, have students block off the eight cells surrounding the highest number
(in this case, any pixels with >7) and check for statistical significance.
See directions in
"Finding a Source". Repeat this
calculation for the CGRO Data
Collected Over 4 Days, and 14 Days.
Ask: during what time interval does statistical significance occur? Answer: it happens between 4 days and 14 days of data gathering.
The students should then determine the minimum number of days
needed to determine the location of a source. They can do this by starting
with 4 days and adding multiples of either 4 hours, 1 day, or 4 days until
they achieve statistical significance. Remind them that they are looking for
the MINIMUM amount of time required for the observation.
Follow up questions:
1. How many separate sources showed up in the final data set?
2. Was the 4 hour set of data useful in any way? (Compare what you get if
you take 6 times 4 hours versus 1 day.)
NOTES TO TEACHER:
From the Data Collected Over 4 Hours, students will not be able to make
accurate predictions even though there are two 3's evident in the data.
There are two sources. The first will appear in the lower right quadrant
after 4 days of data. The second source in the upper left quadrant will
not appear until after 9 days of data. If students round to one decimal
place, eight days of data will demonstrate statistical significance of the
source but for an astronomer, that rounding will alter the significance of
the source. To an astronomer it is very important to be absolutely sure
that a source is located.
ACTIVITY 3: Get the Final Picture
Now we will have the students create an image from the CGRO data collected
over the nine days determined in Activity 2. Images can be created by
using several methods. Have one group use data from Day 1 and multiply it
by 9. The next group should take data from Day 4 and double it then add
data from Day 1. Another group could subtract Day 1 and Day 4 data from
Day 14 or students could subtract 5x(Day 1) from Day 14. Students will
then create color images from the binned data and compare pictures. Use
the following color scale to color a 20x20 grid.
| Black | | 0 - 1.3 |
| Navy Blue | | 1.4 - 10.9 |
| Medium Blue | | 11.0 - 20.0 |
| Turquoise | | 20.1 - 29.6 |
| Green | | 29.7 - 38.1 |
| Lime Green | | 38.2 - 48.3 |
| Yellow | | 48.4 - 57.9 |
| Tan | | 58.0 - 67.0 |
| Orange | | 67.1 - 78.6 |
| Purple | | 78.7 - 85.5 |
| Red | | 85.6 - 94.9 |
| White | | 95.0 - 114.0 |
Below you will find actual CGRO image created by digital pixels using 9 days
of data.
Assessment
Students will look at different parts of the given data to
determine the number of days needed for a statistically significant
source to
appear. For example, use 27 as the most intense (highest number) pixel
in your
block of 9 pixels, and 21 as the maximum intensity level of the nearest
pixels surrounding this block. Use the "short cut" method to determine
when we are
99% sure that we have found a source. If the data from the first set is not
conclusive, double it, and use the "short cut" method once again.
Continue in this manner, until a statistically significant source appears.
Action Plan
Have students visit the Imagine the
Universe! web site and learn more about
high-energy sources. Invite an astronomer or astrophysicist to class to
discuss
the various types of high-energy sources. Invite an X-ray technician to
class to discuss this form of high-energy photons.
Extensions
Students could create a time line for astronomical
discoveries and
superimpose it over a time line of historical events. In art class, students
could create an artist's impression of a nebula, neutron star, black hole
or
other high-energy source. Students could create a short science fiction
story
in language arts class. For additional activities, see the "Language of
Mathematics" teacher's guide from MathVantage, produced by the Math Vantage
Project of the Nebraska Mathematics and Science Coalition, P.O. Box 880326,
Lincoln, Nebraska 68588-0231.
Key Words
high-energy, gamma-rays, X-rays, matrix addition, matrix subtraction, actual
data, satellite, Compton Gamma-Ray Observatory (CGRO), detector,
photon, binned data, cell, statistical significance, statistical analysis,
sigma, standard deviation, normal distribution
REFERENCE:
Statistics Every Writer Should Know , URL:
http://nilesonline.com/stats/index.html
The Math Vantage Project of the Nebraska Mathematics and Science Coalition,
P.O. Box 880326, Lincoln, Nebraska 68588-0231.
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