#### Teacher Guide and Answer Key

Demonstration:Modeling the Earth-Moon System

Materials required:

- 3 cans of Play-Doh
^{TM} - 3.8 meters of string
- 1 toothpick
- If you prefer, you can make your own Play-Doh
^{TM}. The following website lists several recipes for making your own Play-Doh^{TM}or clay material. http://www.kidsturncentral.com/crafts/craftrecipes.htm

If you have the 51 balls of clay ready, this demonstration with discussion takes approximately 30 minutes.

NOTE: You may want to either provide several pictures (models) which contain images of both the Earth and the Moon, and/or have the students find some and bring them to class. After the demonstration, students can compare the different models of the Earth-Moon System and decide which ones best represent the size and/or distance of the Earth and the Moon and which ones are the most misleading.

Pre-Assessment Activity:The Exponential Clothesline

Materials required for each group:

- 1 5-meter piece of clothesline (or string)
- 14 clothespins (or paper clips)
- 14 index cards
- Exponential Clothesline Conversion Table

As explained in The Exponential Clothesline, this is an excellent activity to determine the depth of understanding your students have of exponents and the use of scientific notation. A basic knowledge of exponents is necessary to understand the exponential and linear models of the electromagnetic spectrum which your students are going to construct. This activity can be completed in a 45-minute classroom period.

NOTE: If your students are successful in correctly placing the numbers and exponents on the clothesline, then you may decide not to hand out The Exponential Clothesline Conversion Table. Even if they are successful, the Conversion Table is a good review for fractions and decimals.

Student Handout and Construction of the Electromagnetic Spectrum Model:- You can either have your students construct the template as shown in the diagram in the Student Handout, or you can print out the Model Construction Template and make two additional photocopies of the second page for each group. The students then only have to tape the four pieces of paper together. Without the construction of the template, this activity can be completed in a 45-minute classroom period without the extension, and approximately one hour with the extension activity.
- The students mark off 24 2-cm intervals on the top line of their model and label them as indicated in the directions. They transfer the frequencies for the individual bandwidths in the Frequency Range Table onto this line and label each bandwidth. They should label the entire visible bandwidth of the spectrum, not each individual color within the visible band of the spectrum. They will now have bandwidths that mirror the apparent size of the bandwidths shown on the image at the top of the student handout. The image is an exponential model poster like the one the students just constructed.
- Radio & Microwave 0 - 12.5
- Infrared 12.5-14.7
- Visible 14.66 - 14.87
- Red 14.66 -14.70
- Orange 14.70 - 14.74
- Yellow 14.74 - 14.78
- Green 14.78 - 14.80
- Blue 14.80 - 14.84
- Violet 14.84 - 14.87
- Ultraviolet 14.87 - 16.78
- X-ray 16.78 - 20.00
- Gamma Ray 20.00 -
- The students convert the different frequencies for each of the EMR Bands in the Frequency Range Conversion Table to the same frequency, 10
^{14}. A tutorial for converting exponents is included with the student handout if you decide to include it with the handout. The table below contains the correct conversions.

EMR Bands 10 ^{14}Conversions

(Hertz)Radio & Microwave Near 0 to 0.030 X 10 ^{14}Infrared 0.03 X 10 ^{14}to 4.6 x 10^{14}Visible 4.6 x 10 ^{14}to 7.5 x 10^{14}Red 4.6 x 10 ^{14}to 5.1 x 10^{14}Orange 5.1 x 10 ^{14}to 5.6 x 10^{14}Yellow 5.6 x 10 ^{14}to 6.1 x 10^{14}Green 6.1 x 10 ^{14}to 6.5 x 10^{14}Blue 6.5 x 10 ^{14}to 7.0 x 10^{14}Violet 7.0 x 10 ^{14}to 7.5 x 10^{14}Ultraviolet 7.5 x 10 ^{14}to 600 x 10^{14}X-ray 600 x 10 ^{14}to 1,000,000 X 10^{14}Gamma Ray 1,000,000 X 10 ^{14}to Infinity

NOTE: If your students have not yet encountered converting exponents, you may want to give them the completed table above and simply have them plot them on the model. This activity is about models and they can compare and contrast different models without performing the mathematics. The following URL contains basic information on exponents and a worksheet with answer key for additional practice: http://www.ieer.org/clssroom/scinote.html - - 7. The scale for the linear model is 10
^{14}Hz = 10 cm; the frequencies plotted on the exponential scale result in the following distances from the beginning of the scale:

- Radio/Microwave - 0.3 cm or 3 mm
- Infrared - 46 cm
- Visible
- Red - 46 to 51 cm
- Orange - 51 to 56 cm
- Yellow - 56 to 61 cm
- Green - 61 to 65 cm
- Blue - 65 to 70 cm
- Violet - 70 to 75 cm
- Ultraviolet - 6000 cm or 60 m
- X-ray - 10,000,000 cm = 100,000 m = 100 km
- Gamma Ray - 100 km X 10
^{14}to infinity

NOTE: The students will easily plot the radio/microwave, infrared, and visible bandwidths of the spectrum. They will not start to encounter difficulties until they start to notice that they will not be able to fit the ultraviolet bandwidth on their model. The UV band is actually 60 meters in width. If you want the students to experience the length of the UV band relative to the lower frequency bands they have plotted, have string available for them to measure and stretch out for 60 meters. The X-ray band is 100 kilometers in length; have some local maps and state highway maps available so the students can locate towns that are 100 kilometers away from their school. If you have internet access the students can go to Yahoo Maps and download a map centered on their school.

NOTE: When the students mark a location on the model such as 5.6 x 10^{14}, they will probably place the mark halfway within the frequency range for 10^{14}. This is incorrect. Since this is an exponential model, 5 is actually more than halfway within the frequency range. Whether you bring this to the attention of your students depends upon their level of mathematical understanding. If you have high school students with a good mathematical background, you may elect to have them actually convert the numbers into log values. The conversions are as follows:

- The linear model displays some surprising results compared to the exponential models that are shown in textbooks and on posters. In this model, for example, the radio bandwidth is extremely small, and the visible bandwidth is also small compared to the high energy bandwidths - the high energy bandwidths are huge. This is not a "better" model, it is a difference model. This model is useful in understanding why it is important to study all the electromagnetic emissions from a star, supernova remnant, or galaxy. Studying a deep sky object in only one bandwidth does not give a complete picture of the object - anymore than studying just one system within the human body gives a complete picture of how the human body functions. However, this model cannot fit on a page within a textbook, or even fit on a very long poster. Someone may ask why not have a model that plots the wavelengths of the bandwidths instead of frequency. Frequency is what astrophysicists are most interested in because it is related to energy. A model that uses wavelength instead of frequency would be reversed because the higher the frequency the smaller the wavelength. The higher energy bandwidths would be extremely small and the radio/microwave bandwidths would go to infinity. A model using wavelength would have to reverse the sequence of the bandwidths - the gamma rays would be located at near 0. There are no correct or incorrect answers to this question. The idea is to start students thinking about the models they use and understand their advantages and disadvantages.

EXTENSION: To show students the importance of studying objects in all wavelengths you can find an excellent example here: Cassiopeia A Overlays. This page contains four multiwavelength images of the Cas A supernova remnant. The images are to scale, and can be downloaded and printed on overhead transparencies. The transparencies can then be placed on top of each other on an overhead projector to show how much more information is available for scientists to study when multiple wavelength observations are used. The story of the Cas A supernova event and the historical context of how the remnant first became known as a radio image in 1937 through 1999 when the Chandra X-Ray Observatory imaged the remnant in X-ray and discovered the neutron star in the center is located at http://chandra.harvard.edu/edu/formal/casa_timeline/

Assessment:

EMR Pasta

Materials Required:

- Boxes of different shaped pasta
- Poster paper or pieces of cardboard
- Glue guns or fast-setting glue

The EMR pasta assessment task is an excellent tool to assess student understanding of the distortions contained within models in general, and the electromagnetic spectrum in particular. Students construct their own versions of the electromagnetic spectrum using a variety of pasta shapes, and then present their models and provide an explanation of how their pasta analogy/model does and does not represent the electromagnetic spectrum. The alignments to the National Standards and Benchmarks are included, along with the scoring rubric. This activity can be completed in a 45-minute classroom period.

The Wavelength and Frequency demonstration included with EMR Pasta uses a pasta machine and pasta dough. This demonstration helps students understand that electromagnetic radiation is all the same thing... only the "shape" is different. It is a common misconception that since we "see" the visible spectrum, and "hear" part of the radio spectrum, and get sunburned by part of the UV spectrum - which we cannot either "see" or "hear" that the different bands are not the same phenomena.

NOTE: If you want to involve your students in a more in-depth assessment process you may want to use two other assessment tasks - "Oh Say Can You See" or "Signals from the Cosmos". These assessment activities require students to gather information and construct presentations.

Alignment with national standards

Modeling the Electromagnetic Spectrum: Middle School

Modeling the Electromagnetic Spectrum: High School