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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

  • Two 50 minute periods.

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

  1. 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.

  2. Students will use matrix addition or subtraction to operate on data collected by a gamma-ray detector.

  3. 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

MATERIALS
100 pennies two 6x5 grids per group
5 egg crate separators* labels for egg crates
one transparency per group one TI-82 graphics calculator per group
tape TI-82 instructions for matrix operations
4 hours of CGRO data 1 day of CGRO data
4 days of CGRO data 14 days of CGRO data

* 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

number of pennies in box is number in grid

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.

grayscale - higher number is closer to white

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

  1. 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."

  2. 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.

  3. 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.

  4. 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.

artist concept of CGRO

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.

CGRO data after 9 days
Data After Nine Days

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.

Extension - Using Student Hera to Examine More Images

Student Hera gives students the opportunity to analyze the same data sets that scientists use, using the same tools that scientists use. The Student Hera web pages walk students through examining an image of a supernova remnant to find a suprise in the data.

Take me to Student Hera

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.

If words seem to be missing from the articles, please read this.

Imagine the Universe! is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center.

The Imagine Team
Project Leader: Dr. Barbara Mattson
Curator: Meredith Gibb
Responsible NASA Official: Phil Newman
All material on this site has been created and updated between 1997-2014.
This page last updated: Thursday, 25-Mar-2010 13:56:32 EDT