Engage:

The teacher will lead the class through an engagement exercise dealing with the phases of the moon. With props (flashlight, baseball, and ping pong ball), the teacher will model the phases of the moon with respect to the earth and the sun. The teacher will ask one student to hold a flashlight. The teacher will then hold the moon and earth in different positions and ask the class to discuss how much of the moon will be visible to a person on the earth when it is in each of the locations. This is a really nice engagement.

The teacher will then extend the discussion by asking the students to describe their knowledge of solar eclipses. The teacher will then ask for students to come forward to demonstrate the possible alignment of the moon, earth, and sun during a solar eclipse. Once the student and the audience feel comfortable with the alignment, the teacher will ask another student to explain why this formation causes a solar eclipse to occur. This discussion will serve as a nice transition into the “Exploration” phase of the lesson.

The students might have difficulty seeing the light on the ping-pong ball from far away. Therefore, they will be encouraged to gather around the model.

The students might be aware that the phases of the moon have something to do with the orbit of the moon around the earth, but they might have some misconceptions about why the moon gives off light. As a result of this demonstration, the students should understand that the “moonlight” (as visible from earth) actually comes from the sun.

The students might have difficulty distinguishing between solar and lunar eclipses. Yes, this is quite likely. The teacher will emphasize the difference between the two.

The students should understand - when deciding on the alignment of the earth, moon, and sun - that the moon comes between the earth and the sun during a solar eclipse. At this point in the lesson, however, the students might not understand that the distances between the earth and the sun and between the moon and the earth play critical roles in determining the likelihood of a total solar eclipse.

Explore:

The teacher will assign the students to work groups. The teacher will instruct one student per group to pick up group materials (string, ping-pong, and baseball) and a Results Sheet for each student in the group. Together, the class will discuss the objective - to determine the range of distances (between the moon and the earth) in which a solar eclipse will occur, given a specified distance between the earth and the sun. The teacher will inform the students that they will determine the range three times - once when the distance (earth to sun) is 2 yards, once when 4 yards, and once when 6 yards.

When the exploration begins, the teacher will tell the students to be mindful of using the correct lengths. (In other words, the students need to keep the strings straight. Also, the bottom of the sun needs to on one end of the string and the students should position their eye directly at the other end of the string.)

The teacher will instruct the student groups to begin working on the activity. The teacher will remind the students that they first need to calculate the diameter of the moon and the sun. The teacher will provide the students with no further guidance, but instead allow the students to come up with their own ways of calculating the diameters. The teacher will then walk around the room, answering student inquiries and asking groups probing questions to generate discussion.

The student groups will work together to gather data to record their observations. The students will perform the trials individually, before comparing their results to others in their groups and discussing possible reasons for differences. The Results Sheet will ask the students to identify, for each given earth-to-sun distance, the “cut-off” earth-to-moon distance for a total solar eclipse (the farthest distance that the moon can be from the earth to still have a total solar eclipse). Rather than relying on rulers to determine the “cut-off” distances, the students will calculate the distances between the earth and the moon by using their knowledge of proportion and right triangles. Are these instructions on the worksheet? Also will the kids have to know basic trig ratios to do the calculations? If so, there is a problem since these will be Algebra I students. The students will discuss and record any trends that they might notice when working through the different proportion calculations. Once the student groups have compared their findings, they will record their distance ranges.

Explain:

Together, the class will discuss the results of their explorations. To initiate the discussion, the teacher will ask how the distance from the earth to the moon was calculated. The teacher will ask representatives from each group to share their “cut-off” earth-moon distances and ask the class for possible explanations for differences. The teacher will also ask the representatives to share their fraction of the earth-moon distance over the earth-sun distance for each length of string – 2 yards, 4 yards, and 6 yard. Again, the class will discuss the reasons for variations. I like this discussion about variation and error in measurement. The teacher will ask the students to apply their knowledge of similarity and proportion to the results. The teacher will ask a student to draw a geometrical representation of the situation for the rest of the class. Together, the class use will calculate, using their knowledge of right triangles, the “ideal” distances from the earth to the moon, given the diameter of the moon and the sun as well as the distances from the earth to the sun. The teacher will ask if, given this calculated distance, the students are surprised by their groups’ results.

Since the students were asked to answer relatively open-ended questions on their Results Sheets regarding patterns that they noticed and since the students’ data might have been skewed due to variations in measurements, many students might not have noticed the relationship between the fractions that they calculated.

When the students calculate, as a class, the proportions, they should be able to determine the relationship that exists among the calculated fractions of the earth-moon distance over the earth-sun distance for each length of string - 2 yards, 4 yards, and 6 yards. The students should see that this relationship exists because of right triangles.

Elaborate:

The Teacher will tell students about Angular Diameter and how it relates to the E-S/E-M distance. It will be emphasized to students that since it is very hard to measure size directly of objects in solar system, therefore, we have to use technique that measures angular diameter.

For this activity, the students will be asked to take a piece of string and stretch it from the place they are at all the way to right side of moon. After this stretch another piece of string to left side of moon from the same original point. The students should observe how the angle between two pieces of strings would be 1/2 degrees.

Students will also learn about similar triangles and observe how they all have one angle in common. The teacher will illustrate this feature of similar triangles by drawing an acute angle with two lines on the board. The teacher will explain that the fact that similar triangles have one angle in common is essential for using angular diameters of objects in solar system. The students will explore this by having sun, moon, and earth aligned in such a way that sun is at one end and the earth at the other end make an angle. The moon is at a certain distance from earth such that it blocks the earth. It will allow students to make two similar triangles each with the same angle and will apply to the concept of angular diameter. This is a nice activity to illustrate this concept.

In the end if time permits, the same knowledge will be applied to learn about lunar eclipses.

Student Activity:

The students will use the string and try to illustrate the angular momentum by taking string to two ends of moon. The students observe that the angle between two pieces of string is about 1/2 degrees.

For the second part of the activity, the students will show diagrams of their understanding of similar triangles and angular diameter. The students will label their triangles as ABC and ADE by drawing them on their sheets. Students will measure the distance to the moon and its diameter.