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A student workbook answer key for a NASA Explorer Schools Pre-Algebra Unit lesson on the solar system. It includes pre-lesson activities, planet data sheets for inner and outer planets, and instructions for creating a scale model of the solar system. Students will learn about the distances and diameters of each planet and how to convert between kilometers and astronomical units.
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National Aeronautics and Space Administration
What are the parts of the solar system and how do they compare?
Student Workbook Answer Key: PRE-LESSON Name: Date:
Step 1 : On the back of this paper draw a picture of our solar system. In your drawing, show the different sizes of the planets and where they are located. Label everything. If you have time, add color to your picture. (Student drawings will vary.) Step 2 : Using the chart below, list what you know about our solar system in the column titled “What I know.” In the column titled “What I want to know” write questions you have about our solar system and space exploration. (Possible responses are listed below.)
Student Workbook Answer Key: ENGAGE Name: Date:
Student Workbook Answer Key: ENGAGE Name: Date:
Student Workbook Answer Key: ENGAGE Name: Date:
**Planet Jupiter Saturn Uranus Neptune Pluto Distance from Sun in km 778 million km 1 , 429 million km 2 , 875 million km 4 , 504 million km 5 , 900 million km Distance from Sun in AU
**- 238 º F
Student Workbook Answer Key: ENGAGE Name: Date: ______________
To measure a distance between two objects you need two things: a unit of measurement (how much you are measuring by) and a tool (what you measure with). Long before measuring tools like rulers and tape measures were common, people needed a way to measure things. In early times, people who did not have tools used parts of their bodies (like their thumbs) to measure. About 950 years ago, the width of a person’s thumb was considered an inch. In many languages, the word for thumb and inch are the same or very close. A person’s foot was used to measure feet. A yard was the length from the tip of the king’s nose to the end of his fingertips. Everyone had a way to measure distances, but there was a problem. Everyone knew what to measure with, but there was no standard for how big things were. For example, if you measured the length of your bedroom with your feet, and then your friend did the same with his feet, you would not get the exact same measurement because your feet and your friend’s feet are different sizes. Eventually people agreed on standards—measurements that were the same for everyone. The Romans liked to divide things into units of 1 2. This is why we have 12 months in the year. They decided that a foot contained 12 inches. In England in the 1100 ’s, King Henry I decided to use the Roman standard of measurement for feet, and he spread the word to his people that a foot was 12 inches long. Once the standards were set and everyone agreed on the lengths of units of measurement, the system worked better. In the 180 0’s, the French Academy of Sciences was asked to develop a system of measurement that was based on scientific measurements and used the base- 10 system. The Academy set their standard of measurement (a meter) as a fraction of the distance from the North Pole to the equator on the surface of the Earth. Larger and smaller units were made by multiplying or dividing a meter by factors of 10. One thousand meters is a kilometer. One hundred centimeters is a meter. Ten millimeters is a centimeter. Even the
Student Workbook Answer Key: ENGAGE
Student Workbook Answer Key: ENGAGE Name: Date: ______________
Student Workbook Answer Key: ENGAGE Name: Date:
This sample problem will help you learn to use “ unit ratios” to convert from one unit to another unit. What we know: What we want to know: 1 AU = 150 , 000 , 000 km. Jupiter is 778 , 000 , 000 km from the Sun. How many AU is Jupiter from the Sun? If we want to know how many AU Jupiter is from the Sun, then we need to convert 778 , 000 , 000 km to AU. We can do this using a unit ratio. To convert km to AU, use the unit ratio : 1 AU. 150 , 000 , 000 km This unit ratio is equal to one because 1 AU is equal to 150 million km. When you multiply a distance by this unit ratio, you are multiplying the distance by one. You are not changing the value of the distance. The distance is the same. You simply changed the unit used to measure it.
Student Workbook Answer Key: ENGAGE First, set up the problem. 778 , 000 , 000 km = 778 , 000 , 000 km (^) • 1 AU. 150 , 000 , 000 km Second, cancel the kilometers by marking through the km. = 778 , 000 , 000 km (^) • 1 AU. 150 , 000 , 000 km Third, multiply 778 , 000 , 000 by 1 AU. = 778 , 000 , 000 AU 150 , 000 , 000 Fourth, cancel the zeros by marking through them. = 778 , 000 , 000 AU 150 , 000 , 000 Fifth, divide the numerator (top number) by the denominator (bottom number). = 778 AU 150 Sixth, round to the nearest tenth and state your answer. 778 , 000 , 000 km! 5. 2 AU or Jupiter is approximately 5. 2 AU from the Sun.
Student Workbook Answer Key: EXPLORE Name: Date: ______________
Purpose Now that you have created a scale model of the solar system in terms of size, you need to establish a scale for your model in terms of distance. Then you will need to calculate the distance from the Sun for each planet in your model. Finding the scale between the model of the solar system and the actual solar system is the mathematical challenge of this activity. For a model, the “scale” is the amount by which the size of the original has been changed proportionally. The key to finding the scale distances is using ratios and proportions —relationships between the model distances and the actual distances. Let’s Begin! In your clay model, Pluto is the furthest object from the Sun. For the Clay Model, Pluto is approximately 4 , 205 meters from the Sun. If 4 , 205 meters represents the distance from Pluto to the Sun, then how many AUs are represented by 4 , 205 meters? (Hint: Refer to your Planet Data Sheet – Outer Planets on page 7 .) 4 , 205 meters represents 39. 3 AU. This allows us to set up a ratio. Distance from Pluto to the Sun in the scale model (^) = 4 , 205 _m Distance from Pluto to the Sun in the solar system 39. 3 AU
Student Workbook Answer Key: EXPLORE The relationship between 4 , 205 m and 39. 3 AU will be our scaling ratio. We can use this relationship to find the distances from all of the planets to the Sun in the model. Begin with the information you know: 1. What is the distance between the Earth and the Sun? 1 AU 2. The scaling ratio for this model is: 4 , 205 m 39. 3 AU Next, to find the scale of the model, we want to know how many meters represent 1 AU? Step 1 : Set up a ratio of the distance from a planet to the Sun in the model and the distance from a planet to the Sun in the solar system. Write an “x” in the gray space below to represent the number we do not know. Distance from Earth to the Sun in scale model (^) = x m Distance from Earth to the Sun in solar system 1 AU Step 2 : Set this ratio equal to the scaling ratio. Distance from Pluto to Sun in model (^) = Distance from Earth to Sun in model .Dist. from Pluto to Sun in solar system Dist. from Earth to Sun in solar system 4 , 205 m (^) = x. 39. 3 AU 1 AU
Student Workbook Answer Key: EXPLORE Name: Date: ______________
Based on the scale diameter of the clay planets, it has been determined that the scale distance of the clay model of the solar system is 107 meters. This represents 1 AU in our solar system. Use this information to:
Meter Paces from Sun
from Previous Object Sun** 1, 39 1, 900 993 — — — — Mercury 4, 878 3. 5 0. 4 43 86 86 Venus 12, 104 8. 6 0. 7 75 150 64 Earth 12, 755 9. 1 1. 0 107 214 64 Mars 6790 4. 8 1. 5 161 322 108 Asteroid Belt 1 to 1, 000
Student Workbook Answer Key: EXPLORE Name: Date: ______________
Purpose Now that you have created a scale model of the solar system in terms of size, you need to establish a scale for your model in terms of distance. Then you will need to calculate the distance from the Sun for each planet in your model. Finding the scale between the model of the solar system and the actual solar system is the mathematical challenge of this activity. For a model, the “scale” is the amount by which the size of the original has been changed proportionally. The key to finding the scale distances is using ratios and proportions —relationships between the model distances and the actual distances. Let’s Begin! In your 1000 - meter model, Pluto is the furthest object from the Sun. For the 1 , 000 - Meter Model, Pluto (small pin head) is approximately 1 , 000 meters from the Sun (bowling ball). If 1 , 000 meters represents the distance from Pluto to the Sun, then how many AUs are represented by 1 , 000 meters? (Hint: Refer to your Planet Data Sheet – Outer Planets on page 7 .) 1 , 000 meters represents 39. 3 AU. This allows us to set up a ratio. Distance from Pluto to the Sun in the scale model (^) = 1 , 000 _m Distance from Pluto to the Sun in the solar system 39. 3 AU
