# Teaching Tips

This section contains specific tips for teaching the project- facts your students may need to know as they work and advice for solving common problems students and teachers may encounter.

## Introduction

A good place to begin to teach this project is by determining what background knowledge your students have about what the universe is- and isn’t. The first lesson begins with having the students complete the first two sections of a “KWL” (What I Know, Wonder about, and Learned) about the universe. This provides valuable insight to the teacher on the range of background information that the students have, and what misconceptions they might also possess.

This is an excellent project to use with students who have differing levels of background information and ability levels. When this project is taught in a setting that allows students to self-pace themselves by working on individual/in pairs on computers, the teacher can assess the content and skills that individual and small groups of students need to grasp the content and skills. More capable students can move ahead and can complete optional research challenge problems and activities.

In an ideal setting, the teacher would begin the class session by having one computer hooked up to a projection device that enables the whole class to see what is on one computer screen. At that point, a directed mini-lesson would occur in which the teacher gave a brief overview of the activities that the students would engage in during that class session. Mini-lessons could be conducted to focus on areas of difficulty for some students by letting the more capable students explain how they reached their solutions to specific problems and exercises. Teachers could use this whole class projection system to review, reteach, and assess how the students were doing on the content they had covered in previous lessons.

After working as a class on those concepts as a whole class, the students could work independently at their own pace on individual computers. The teacher would be free to circulate around the class and assist those students who needed further explanation. Peer tutors could also be enlisted to assist students.

## Your Cosmic Address

Many students really do not understand that they live on a planet that revolves around the Sun, which is just one of billions of stars in the Milky Way galaxy, which is just one of billions of galaxies in the universe! Actually, a lot of adults don’t really understand this either!

Therefore a great place to start is to help them find their place in the universe by doing this very concrete activity. Depending on your students’ background knowledge, you may want to spend some time reviewing celestial objects (objects that are in space) and how they differ (i.e. how a star differs from a planet, how a solar system is just one of billions of possible solar systems in a galaxy, etc…). One good strategy is to allow other students to share their expertise in this area b calling on them to explain some of these concepts. Most students find space intrinsically fascinating, but some students may feel that astronomy is too “difficult” for them to understand. It is good to help them feel successful and intrigued from the start!

## How Big Is It?

In addition to not really knowing where we fit into our universe, most people are unaware of the vast expanses of empty space in our universe. A good starting point here to have the students demonstrate how far away they think the Sun is from the Earth if the Sun were the size of a basketball and the Earth was the size of a dot at the end of this sentence. After they have demonstrated their predictions, explain to them that the Sun would be about 23 meters away.

Discuss the need for measuring things in light years, and talk about the fact that a light year is how far light travels in one year. Explain that light travels from the Sun in only 8 minutes, and that it travels at 300,000 kilometers per second! Ask how far away they think the next closest star is.

The farthest things we see are quasars; ultrabright objects that astronomers think are actually caused by matter falling into giant black holes. For more information, see the SkyServer Quasars project.

Help them understand the need to use scientific notation when working with such vast distances in space. If you have not yet studied scientific notation, you may wish to introduce it quickly before students do Exercise 1; although, students can skip Exercise 1 without losing the logic of the Project.

Exercise 1 should show them the usefulness of scientific notation: it’s much easier to write “1.42 x 10^{23}” than to write “142,000,000,000,000,000,000,000.”

## Expanding Universe

It is very useful to use models to understand things that are too large to actually recreate or observe. Discuss the usefulness of models in science. You may need to assist students as they complete their models of the expanding universe. Some may find it difficult to place the dots and their labels on the balloons, and others may require assistance calculating the average speed of each dot with respect to the “Milky Way.” You could assist those students who are having difficulty with this by doing this activity in a directed format rather than having them complete it using their own data.

After they completed the balloon activity and noticed that the dots were moving away from each other, they could put the balloons away and use the same set of data to calculate the speed, collect the data, and create the graph. Depending on their grade level and experience with graphing, some students might benefit from having the graph prepared ahead of time, and they would plot the data points.

## How Do We Know?

This is a good point to review the scientific method. At this time, the students should be reminded that they will be using actual data as they learn about the expansion of the universe. They will be following some of the same steps that astronomers followed to make this discovery. If time permits, you could explain in greater depth what the Sloan Digital Sky Survey is (see About the SDSS and/or encourage your students to take some time exploring this section.

## Distances and Magnitudes

Some students may require some concrete experiences with understanding the difference between actual and relative distances. They could replicate the activity shown with the Coke cans to deepen their understanding in this area.

Some students may have difficulty understanding the factor of 2.51 in the scale of magnitude. Explain that some other scales work similarly: in the Richter scale, a magnitude 7 earthquake is 10 times stronger than a magnitude 6. In the decibel scale, a 100 decibel sound is 10 times louder than a 90 decibel sound. Likewise, a magnitude 6 star or galaxy is 2.51 times brighter than a magnitude 7 star/galaxy.

Tell students that each wavelength of the SDSS survey (u,g,r,i,z) has its own magnitude. They should use the green-wavelength magnitude (g) for Exercise 2, but they could use any of the five if they wished.

Make sure students understand the difference between absolute and relative distance. Have them explain why the Hubble diagram requires only relative distance. Have them study the picture above Exercise 2.

The key to doing Explore 4 is using the Navigation Tool. See the Navigation Tool help for more information. Many students would benefit from having a directed mini-lesson on using the Navigation tool, and on opening up and then reading the data in the Object Explorer.

Suggestions for doing this mini-lesson are located in the Lesson Plan page, under the Procedure for “Lesson 2.”

## Redshifts and Spectra

Be sure students understand the concept of redshift before you discuss spectra. Remind them that looking at spectra is a way to measure redshift: spectral lines serve as markers for how redshifted a galaxy is.

The fact that redshift can be interpreted in two ways is a subtle but important point. When objects are close to Earth, their redshifts should be interpreted as coming from Doppler shifts due to relative motion. When objects are across the universe, their redshifts should be interpreted as coming from the cosmological stretching of space. Be sure that students understand the concept of the stretching of space, because they will need it to understand the Big Bang in the next section.

Tell students that spectra are one of the most important tools that astronomers use. In addition to redshift, spectra can tell astronomers the temperatures and compositions of stars and galaxies.

Many students will not have seen spectra before. To familiarize them with spectra, you could make a color transparency of the spectra in this section, and spend some time describing the data. Point out the redshift data (bottom right-hand corner of spectra image, “z” value). Be sure they know how to find the redshift data to use in the “Explore 5” activity.

## Making the Diagram

Explore 6 gives instructions on how to use Microsoft Excel. If you use a different graphing program, you may want to give students a quick tutorial before beginning the project, or before beginning Explore. 6 While it is good for students to be able to create graphs themselves, it is not vital to understanding the content in this project. For those students who are not ready to use computerized graphing functions, they can use the good old graph paper and pencil method and still be successful with this exercise.

You may need to help them develop their graphs by telling them to place the magnitude (in g) along the x axis, and the redshift along the y axis. Some students will also require assistance determining the increments to use on their graph. Teach students the importance of making a graph clean and readable for other scientists.

A “model” is a theoretical explanation for the relationship seen in the data. In the case of the Hubble diagram, scientists use a linear model forredshift as a function of distance – they assume that the underlying astrophysics is such that redshift will be linearly dependent on distance. Note that the mathematical model, by itself, says nothing about the underlying astrophysics; it says only that the laws should be such that they will produce a linear relationship between distance and redshift.

To test whether a model is a true description of data, scientists test the “fit” of the model. They find a trend line – the line that comes closest to fitting through each data point. Then, they calculate the distance the line falls from each actual data point.

## Diagram and Expanding Universe

In this section, it is important that they understand the concept of “point of reference.” Spend some time making sure they understand that we are not at the center of the universe (as much as we like to believe we are!).

Be sure they understand why they plotted magnitude against redshift, and ask questions to determine if they can explain what the trend line in their Hubble diagram is describing. This section offers a good place to point out how interconnecte mathematics and science are, and to understand the fact that mathematics helps us to describe relationships that exist in our natural world. Students may enjoy understanding the equation for the trend line, and may benefit from putting the separate components (“c”, “z”, etc…) of the formula on index cards and then having them demonstrate where they go and what they stand for.

## The Big Bang

It is important to emphasize that the “big bang” was not an explosion – it was just the time when the universe started expanding. Have students think about the differences between the explosion model and the big bang model. How could you tell, based only on what you can see and measure from Earth, which model correctly describes our universe? Remind students that the process of deciding between models based on observable evidence is at the heart of the scientific method.

Some students whose mathematics skills are low may benefit from doing the exercises in the “Absolute and Relative Distances” in a directed setting, as it does require them to perform mathematic equations involving scientific notation. Remind students of the difference between relative and absolute distance. Astronomers do know absolute distances to some galaxies, based mainly on looking at apparent magnitudes for known types of stars. From these absolute distances, they can use the equation to find a numeric value for H0. Finding the value of H0 has been an important project in the past decade.

## More Galaxies and Research Challenges

These activities will primarily be for students who were able to proceed through the previous exercises and are ready to attempt more challenges. This is a good place for teachers to work with those students who need more assistance grasping the previously introduced concepts and skills, and allowing the more capable students to continue ahead independently. The “Explore 7” activity would also be a useful activity to teach in a directed format with students who need more practice with data collection and graphing.

The next two Research Challenges help you understand some of the complexities of the Hubble diagram.