Solar System Math

[Pages:36]National Aeronautics and Space Administration

NASA Explorer Schools Pre-Algebra Unit Lesson 1 Student Workbook

ANSWER GUIDE

Solar System Math

Comparing Size and Distance

What are the parts of the solar system and how do they compare?

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Student Workbook Answer Key: PRE-LESSON

Name:

Date:

Pre-Lesson Activity

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.)

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Student Workbook Answer Key: PRE-LESSON

Name:

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Math Review: Converting Units

Length

Volume

1 kilometer = 1,000 meters 1 gallon ! 3.78 liters

1 meter = 100 centimeters 1 gallon = 4 quarts

1 centimeter = 10 millimeters 1 quart ! 0.95 liter

1 mile = 5,280 feet

1 liter = 1,000 milliliters

1 yard = 3 feet

1 pint = 0.5 quart

1 meter ! 3.28 feet

1 pint = 16 fluid ounces

1 foot = 12 inches

1 inch ! 2.54 centimeters

Mass

1 pound ! 454 grams 1 kilogram = 1,000 grams 1 gram = 100 centigrams 1 centigram = 10 milligrams

Directions: Use the table of relationships above to solve practice problems 1-5 below. You may use additional paper for doing calculations.

1. Yna bought 3 gallons of milk at the store. How many liters did she buy? Approximately 11.3 liters

2. Jamal caught a pass and ran 57 yards to make a touchdown. How many feet did he run? 171 feet

3. A car weighs 850 pounds. How much does it weigh in kilograms? (Hint: change pounds to grams, then change grams to kilograms) Approximately 386 kilograms

4. Jessica runs the 100-meter dash at the track meet. How many feet does she run? Approximately 328 feet

5. Bonus Question: Juan and his family traveled 339 miles from San Jose to Los Angeles. How many kilometers did they travel? Approximately 546 kilometers

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Student Workbook Answer Key: ENGAGE

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Travel Planning

1. If you planned a family vacation, how would you decide where to go?

Possible responses: Ask family about places that interest them; Consider locations that were within budget; Pick a theme such as "national parks" etc.

2. What factors (details about your trip) would you need to think about?

a. Cost

c. Activities/ entertainment

b. Distance/ travel time

d. Weather/ climate

Space Exploration

3. What are some reasons for humans to explore our solar system?

Thoughts to share: Human exploration will not only help us to answer scientific questions, but will also advance engineering and technology. Many new technologies have been made possible by the space program, including dental braces, rechargeable batteries, cordless power tools, wireless telephones, satellite television, quartz watches, household smoke detectors, fireproof clothing, cardiac monitoring equipment, and even the global communication systems used to guide you through your neighborhood. For every dollar the U.S. spends on the space program, it receives $7 back in the form of corporate and personal income taxes from increased jobs and economic growth.

4. Why should humans explore space in addition to robots?

Thoughts to share: One reason NASA wants to send humans is that they can make judgments and can adapt to changing situations. Making observations and understanding what you see is easier, more efficient, and more exciting in person, instead of through pictures or data. In terms of analysis and studying samples, it takes a Mars Exploration Rover (MER) an entire Mars Day (almost 25 hours) to do what a field geologist can do in 30 seconds. Ask the students to calculate the following: (Students may want to use ratio and proportion to find the answer.)

Question: In just 5 minutes, how many days worth of MER work could a geologist do? Answer: In 5 minutes a geologist could do 10 days worth of rover (robot) work.

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Student Workbook Answer Key: ENGAGE

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Our Solar System

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Student Workbook Answer Key: ENGAGE

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Lesson 1 Planet Data Sheet ? Inner Planets

Planet

Mercury

Venus

Earth

Mars

Distance from Sun in km

58 million km

108 million km 150 million km 228 million km

Distance from Sun in AU

0.4 AU

0.7 AU

1.0 AU

1.5 AU

Diameter in km

4,878 km

12,104 km

12,755 km

6,790 km

Avg. Surface Temperature

Atmosphere

662? F 350? C

869? F 465? C

59? F 15? C

-9.4? F -23? C

None

Mostly Carbon Mostly Nitrogen Mostly Carbon

Dioxide

and Oxygen

Dioxide

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Student Workbook Answer Key: ENGAGE

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Date:

Lesson 1 Planet Data Sheet ? Outer Planets

Planet

Jupiter

Saturn

Uranus

Neptune

Pluto

Distance from 778 million 1,429 million 2,875 million 4,504 million 5,900 million

Sun in km

km

km

km

km

km

Distance from Sun in AU

5.2 AU

9.5 AU

19.2 AU

30 AU

39.3 AU

Diameter in km 142,796 km 120,660 km 51,118 km 49,528 km

2,300 km

Avg. Surface Temperature

-238? F -150? C

-292? F -180? C

-366? F -221? C

-391? F -235? C

-382? F -230? C

Atmosphere

Hydrogen & Helium

Hydrogen & Helium

Hydrogen & Helium

(methane)

Hydrogen & Helium

(methane)

Thin, freezing methane

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Student Workbook Answer Key: ENGAGE

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Date: ______________

A Brief History of Units of Measurement

Student Reading

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 12. 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 1800'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

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