1. Investigation 4
Part 2: How big/how far?

2. Review Moon Data Moon diameter: 3,474 km Moon distance: 384,000 km
Update Moon Log
Take a few minutes to have a student update the class Moon Log. Remind students to keep up with their daily observations.
2. Review Moon data
Have students open their notebooks to review the size of the Moon and its distance from Earth. As students report the diameter and distance, write the two data on the board.
Moon diameter: 3,474 km
Moon distance: 384,000 km

3. Focus question What does a scaled Earth/Moon model look like?
Tell students,
“We know how big the Moon is, and how far it is from Earth, but I’m wondering,
What does a scaled Earth/Moon model look like?”
Hold up one of the small Earth globes. Tell students,
“We have a model of Earth, but we don’t have a model Moon. What is a model? It’s an accurate representation of an object or system. It can be larger than reality, like a model of an atom or a cell. Or it can be smaller, like this model of Earth. You will need to make a scaled model of the Moon to go with the model of Earth. Then, you will have to position your model Moon at the proper distance from model Earth to represent the distance from Earth to the Moon.”
“With a scaled model of the Earth/Moon system, we will have a better sense of the size and distance relationships between Earth and the Moon. Once of the first things you will need to do is to find the scaling factor, which is the ratio of the real size to the model size.”
Write or project the focus question on the board. Have students record the focus question in their notebooks. They should also define scaling factor and add the word to their vocabulary indexes.

4. Scaling Factor
The ratio of the real size of an object to its modeled size.

5. Scaling 4. Review scaling (optional)
If students are weak in scaling and need a refresher, or if you want to emphasize the math and proportional reasoning in this investigation, plan to use notebook sheets 23 and 24, Calculating a Scaling Factor A and B, at this point in class.
Challenge students with Calculating a Scaling Factor A, and step them through the process with Calculating a Scaling Factor B if needed.

6. Earth/moon model
How big do you think the Moon would be, and how far away from Earth would it be?
5. Discuss constructing an Earth/Moon model
Hold up a sheet of aluminum foil or a handful of toilet tissue. Propose using it to make a model Moon to be a scaled companion for the Earth globe. Ask question on slide.
Draw a circle about 12 cm across (the diameter of the little Earth globe). Have students use the space in their notebooks below the focus question to record their predictions for how large the Moon would be to accompany this model Earth and how far away from Earth would it be.
Call on a volunteer to draw a circle on the board to represent the proper size and distance for a scaled Moon. (They will probably make the Moon too big and place it too close to Earth.) Ask students to remember this model.

7. Earth’s diameter Earth diameter: 12,756 km 6. Record Earth’s diameter
Students have information about the Moon’s diameter and distance from Earth from Part 1, but they will need an additional bit of information: Earth’s diameter. Write the information on the board.
Earth diameter: 12,756 km

8. 7. Develop a plan
Make sure students have access to measuring tools and calculators. Visit with each group as they begin gathering the information they need. Ask questions to focus them on what they already know and what they need to find out. Distribute materials so students can start measuring globes and planning what to do. Remind students not to make their Moon models until they’ve calculated what size to make them. If you’re using toilet tissue and water, have the water measure and in cups so each group gets just the amount needed for the activity.
TEACHING NOTE:
Students may need a fair amount of scaffolding with this activity. Teacher master I (on slide) will allow you to walk students through step-by-step. Blanks are let for each calculation students will complete. Teacher master J can be used to confirm correct answers.
Alternatively, you might want to write a list of the unknown information on the board, next to the known information. For example,
Moon diameter = 3474 km
Moon model diameter =
Moon distance = 384,000 km
Moon model distance =
Earth diameter = 12,756 km
Earth model diameter =
Then you can prompt students to look for the “unknown” information that they can easily determine (the diameter of the Earth model), which will allow them to determine a scale ratio.
Actual kilometers/model centimeters
(12,756 km/12 cm = 1063 km/cm)
They can use the ratio to calculate the remaining numbers.

9. Measure Earth-globe diameter
Record the diameter or circumference of the globe.
Record your technique for measurement.
8. Measure Earth-globe diameter
Students will usually begin by trying to measure the diameter or circumference of the globe. It can be difficult to measure the diameter of a sphere with a conventional ruler or meter tape. If students are having trouble, show them a few techniques. Here are three possibilities:
Pile up books until the globe will just fit under a ruler extending out from the top of the stack. Then measure the height of the stack.
Remove one of the plastic plugs from the globe, and use a straw like a dipstick to measure the diameter accurately.
Measure the circumference with a meter tape or by rolling the globe across a surface. Divide that by pi (d=c/pi)
TEACHING NOTE
Encourage students to record their techniques used for measurement and all their calculations in their notebooks.

10. Monitor progress 9. Monitor the activity
Circulate among the groups to monitor their progress. Look for these measurement results.
The globe is about 12 cm in diameter. Earth is 12,756 km in diameter. Each centimeter on the globe equals 1063 km on Earth. This makes the globe roughly 1/10,000,000 the size of Earth.
The Moon is 3474 km in diameter (a little more than ¼ the diameter of Earth). The model Moon should be about 3.3 cm in diameter (about the size of a table-tennis ball) to be properly scaled to the Earth globe.
The Moon is about 384,000 km from Earth, so the model Moon should be about 361 cm (3.6 m) from the globe.
If students are off significantly with any of these scale-model dimensions, decide how you want to deal with the situation. Here are a couple of options.
Ask the groups to revisit their calculations
Let the groups complete their models, and then have a class problem-solving session to correct the models.

11. What to look for 10. Provide a more structured approach (optional)
If students stumble on the proportional mathematics, consider using teacher master I, Earth/Moon Model, to guide students step-by-step through the process. Teacher master J is the same sheet with answers provided.
11. Assess progress: scientific practices
Assess students’ understanding of the relationships between Earth and the Moon in constructing models.
WHAT TO LOOK FOR:
Students have accurately measured the diameter of the Earth globe.
Students have used one of several methods to set up a ration to calculate the diameter of the Moon model and its distance from the Earth globe.
The Moon model is approximately 3.3 cm in diameter and placed about 361 cm from the Earth globe.
Observe students’ models, checking the size of the Moon and the distance between the Moon and Earth. Stand back to get a sense of how motivated students are to achieve a satisfactory outcome. Make notes on the Scientific Practices Checklist while students work.

12. Finished models Are the Earth models all the same size?
Are the Moon models all about the same size?
Are the Moon models all located at about the same distance from the Earth models?
12. Review the finished models
Make sure that groups have time to finish their model Moons and place them the appropriate distance from their model Earths. Ask students to look at the different models created by the groups. Ask questions on slide.
Answers:
Yes
Varies
The answers to the second and third questions depend on the method used to arrive at the Moon size and orbit radius. If there is variation, ask students to describe their methods to the rest of the class. Work on the problem until all groups agree on an acceptable model.
---POSSIBLE BREAKPOINT---

13. Revisit the focus question
What does a scaled Earth/Moon model look like?
13. Answer the focus question
Give students a minute or two to appreciate the immense distance between Earth and the Moon. Have them return to their predictions from Step 5, and compare those predictions to the class’s consensus model of the Earth/Moon system.
Ask students to answer the focus question, based on their new understanding.

14. New Strategy
What is the distance from Earth to the Moon in Earth diameters?
14. Introduce a new strategy
Tell students,
“I know a shortcut for making an Earth/Moon model. We know how far away the Moon is in one unit – kilometers (384,000 km). We can also express the distance from Earth to the Moon in other units.”
“Let’s use the diameter of Earth as our standard unit (instead of kilometers or centimeters).”
Ask question on slide.
Give students a chance to think about how to approach this problem. If necessary, give them some guidance.
Ask students to calculate the distance from Earth to the Moon in Earth diameters by dividing the distance to the Moon by the diameter of Earth. The Moon is about 30 Earth diameters away.
Challenge students to figure out the diameter of Earth in Moon diameters (by dividing the diameter of Earth by the diameter of the Moon). Earth’s diameter is 3.6 times the diameter of the Moon or, grossly round off, about 4 times the diameter of the Moon. It follows that the Moon is very roughly one-fourth the diameter of Earth.
By using these two relationships, any number of Earth/Moon models can be constructed by identifying one sphere as Earth, finding a second sphere about one-fourth that size, and positioning it at a distance about 30 times the diameter of the Earth sphere. This will give you a rough model of the Earth/Moon system.
Estimate the dimensions of additional Earth/Moon models using some classroom objects as representations for Earth and/or the Moon (an orange, basketball, marble, beach ball, or globe).

15. If the Earth is modeled at 23 cm in diameter, what size would the moon be and how far apart would the two be?
If the Moon sphere is 23 cm in diameter, how big would the Earth sphere be and how far apart?
If the Earth/Moon spheres are 100 m apart, what are the diameters of each?
15. Reinforce Earth/Moon relationship
Propose a couple of puzzles for students to solve in class or as homework.
On slide.
Answers:
Moon about 5.5 cm and 690 cm apart.
Earth about 1 m in diameter and 30 m apart.
Earth sphere about 3.3 m in diameter, Moon about 0.8 m.