LESSON: PLANETS IN PROPORTION
By Idania Dorta, former Math teacher and Mathematics Consultant for Glencoe/McGraw-Hill Publishing.

Time: One class period

Background

In August, Mars made its closest pass to Earth in nearly 60,000 years, giving observers a chance to get a good look at the red planet without having to use telescopes. Normally, Mars is about 140 million miles away from Earth, but it orbited a mere 34 million miles away. So that we have a better idea of the distance between Earth and Mars, the moon is only 240,000 miles away.

Lesson Overview

The following lesson looks at the distance and relative size of the rest of the planets with respect to Earth and the Sun. The activity will give students an appreciation of the vastness of their universe and the minuteness of their part in it. Students will discover scales for both the solar bodies' relative sizes and their distances from the Sun. Students will find equatorial circumference and volumes of the solar bodies. They will apply estimation strategies and proportional reasoning to determine a scale comparing the planetary bodies to Earth. Students will convert measurements of time and distance using scientific notation. Both the metric and customary units will be applied. Students will determine the time required to reach other planetary bodies from Earth using different modes of transportation.

Correlation to National Standards

Materials:
-Paper, pencil, calculator, solar system poster (if available)
-Student worksheets and teacher answer keys (provided in printer-friendly pdf format):

• Planets in Proportion directions
• Formulas sheet
• Solar System in Miles worksheet
• Solar System in Miles answer key
• Solar System in Kilometers worksheet
• Solar System in Kilometers answer key

Procedure

1. Distribute the materials that include Planets in Proportion Directions, Formulas Sheet, Solar System in Kilometers, and Solar System in Miles worksheets.

2. Ask a student to read the directions aloud and answer any clarification questions.

3. Discuss terminology references.

4. Depending on the class size, create cooperative learning groups (preferably 10 groups, one for each of the planets). Each group is assigned one of the 10 solar bodies and performs the estimations as stated in the directions.

5. Assign numbers to the members of each group (1-3 or 1-4, depending on the number of students in each group). Each group member is responsible for a particular calculation associated with each planet.

6. Call a group member number out loud. That group member must meet with his peers from the other assigned groups and report back to his/her group with the findings of the information about their solar body. (This way, each member is responsible for gathering information and communicating about mathematics and science with others.)

7. Repeat step 6 nine more times.

8. Have students complete the calculations on the Solar Systems worksheets. A teacher answer key is provided in the materials section of the lesson.

9. Lead a discussion about the estimations for each solar body's unknown value; students should explain how they arrived at their estimates and ask any clarification questions.

10. By referring to the column labeled "Diameter with respect to," determine a scale to use in reference to the relative sizes of the planets and the relative distances of the planets from the Sun if you were to create a poster of the solar system.

Instructional Strategies
Cooperative Learning Groups, Jigsaw

Assessment

Use the student worksheet as the assessment and/or pose the following questions:

• Explain how you chose the scale for the planets.
• Explain how you chose the scale for the distances.
• How did making the model of the solar system change your understanding of its size?
• What is the literal meaning of when you gaze into space and are "looking back in time"?
• Does rounding a measurement to the millions create a significant measurement error? Explain.

Extension Activities:

1. Have the students use their size ratios to create the solar system on a poster board or using objects that would represent the planets. Ask the students to explain how they chose the scale for the planets.

2. Have the students use their distance ratios to create the solar system on a poster board. Have the students explain how they chose the scale for the distances. Their answers will vary. Their explanation should include proportional reasoning.

Correlation to National Standards
NCTM Principles and Standards for School Mathematics
http://standards.nctm.org

Number Sense

Understand meanings of operations and how they relate to one another

• Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

Compute fluently and make reasonable estimates

• Judge the reasonableness of numerical computations and their results.

Measurement

Understand measurable attributes of objects and the units, systems, and processes of measurement

• Make decisions about units and scales that are appropriate for problem situations involving measurement.

Apply appropriate techniques, tools, and formulas to determine measurements

• Analyze precision, accuracy, and approximate error in measurement situations.
• Use unit analysis to check measurement computations.

Author Idania Dorta is a Mathematics Consultant for Glencoe/McGraw-Hill Publishing. She has a Bachelor's Degree in Mathematics Education from Florida International University and a Master's Degree in Computer Applications in Education from Barry University. Her experience includes teaching at the middle and senior high school level as well as staff development and training of teachers.

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