# Using Density to Predict Planetary Differentiation

Ashley Lagas

AshleyR.Lagas@gmail.com

Earth and Space Science 2011

NSF, MIT, UMass Amherst STEM Program

Elkins-Tanton, Tanton, and Doris

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#### Summary

This is an inquiry based lesson designed for middle school students (7th grade) who are already familiar with states and properties of matter. This lesson serves as an informal assessment of students' understanding of density, elements and also serves as an introduction to planetary formation.

In this lesson, in lab groups, students determine how to measure and calculate the density of 3 different materials. Once the densities are calculated, students should apply what they know about density in order to make predictions of how these materials would differentiate during a planet's formation.

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## Learning Goals

Objectives:

-Students identify the best method to calculate mass and volume of 3 different materials

-Students calculate the densities of materials

-Students predict how a planet's composition will possibly differentiate during a planet's formation

-Students calculate the ratio of material-composition of planets

## Context for Use

This lesson is an inquiry based lab activity designed for Middle School aged students, specifically 7th grade students in one 50 minute class period. Depending on class size, students can be placed in partners, or groups of 3 or 4. Lab equipment necessary include: triple beam balance or electronic scale, measuring tape, rulers, water, graduated cylinders, and any other lab equipment available in order to supply students with enough varying equipment that they can choose the best tools necessary to measure and calculate density. The iron ball bearings are intended to represent the iron core (most dense), the fish pebbles will represent the mantle (less dense than iron, more dense than rock pebbles), the rock pebbles will represent the crust (least dense).

Before completed this lesson, students should already have an understanding of the properties and states of matter, so that students can apply this knowledge in this lesson. Students should already have an understanding of how different elements on the periodic table have different atomic masses and that molecules of different substances move differently in the solid, liquid, and gas phase.

This lesson is anticipated to be completed as a review of properties of matter and as an introduction to planetary science, specifically to the formation of planets and the differentiation of materials into layers during a planets formation.

## Background

Properties of Matter: Density=Mass/Volume

Earth and Space Science: During a planet's formation (molten stage) the materials of the planet will differentiate into different layers based on density differences and the force of gravity. The densest materials would form the core or center of a planet, and the least dense materials would stay "afloat" and would form the other layers of the Earth, specifically the mantle and the outer layer of a planet, or crust. *Please Note: The crust may or may not form during magma solidification, but this activity utilizes three different materials that could model how the materials in each of the layers of the Earth have different densities, with the most dense materials found in the core of a planet.

## Description and Teaching Materials

### In-Class Activities

Part I: Calculating Density

- Students are supplied with various instruments of measurement, and students must determine with their lab groups the best method to calculate the density of the 3 lab materials: ball bearings, rock pebbles, and colorful fish tank pebbles.
- Students complete a data table of all of their measurements, as well as their calculated densities of the lab materials. Students are required to write out all of their mathematical calculations to show their work.

Part II: Calculating Ratios of Planetary Compositions

- Students are supplied with the average densities of different planets and are also given the densities of two materials that make up the planets.
- Students calculate with their lab groups the ratio of the two materials that make up the different planets and predict how these materials will differentiate into layers when the planet formed.

### At Home Assignments

If students do not finish any laboratory analysis in class, students can complete this at home for homework.

### Materials

-triple beam balance or electronic scale

-measuring tape, rulers

-water

-graduated cylinders

-stop watches

-beakers

-rock pebbles

-colorful fish tank pebbles

-ball bearings

-calculators as needed

## Standards

Massachusetts Science and Technology/Engineering Curriculum Framework, October 2006:

Earth and Space Science, Grades 6-8: The Earth In the Solar System, Learning Standard 8. Recognize that gravity is a force that pulls all things on and near the earth toward the center of the earth. Gravity plays a major role in the formation of the planets, stars, and solar system and in determining their motions.

Earth and Space Science, Grades 6-8: Earth's Structure, Learning Standard 2. Describe the layers of the earth, including the lithosphere, the hot convecting mantle, and the dense metallic core.

## Teaching Notes and Tips

In order to support students, teachers can give examples of previous density activities completed in class to refresh students' memories if they are having difficulty determining what measurements to take. For example, ask students, "What happens to the level of water in the bathtub, when someone gets into the bathtub."

This lesson can also be used to practice using measurement tools in a science classroom and to practice calculating density versus expecting students to come up with the measurement techniques necessary to calculate density. This would essentially eliminate the inquiry-based portion of this lesson, and thus the lesson would turn into a lab activity with more teacher guidance of how to calculate density.

## Assessment

The lab exercise itself, can serve as an informal assessment of students understanding of the concept of density. Students' critical thinking skills can also be assessed when students apply what they know about density to how the layers of planets are formed during a planet's formation.

## References and Resources

Elkins-Tanton, Linda T. The Earth and the Moon. New York: Facts on File, Inc. 2010.

## Using Density to Predict Planetary Differentiation --Discussion

Ashley, this is a really interesting open-ended, experimental-style activity. I'm very eager to hear how it goes! Here are some comments:

In the summary, perhaps you could talk a little more about what the students should know about "states and properties of matter" before they begin here.

I worry that the students will not be able to do this in 45 minutes. Do you think it'll fit?

Under Background: Your description is fine, except the lighter "floating" materials are the planet's mantle, not necessarily the crust. The crust of a planet may or may not form during a magma ocean solidification.

I am not sure what the purpose of the three materials are. Ball bearings, as long as they are predominantly iron, represent the core. What do the two others represent? What are fishtank pebbles made of? You might want a basalt (lava), kind of representative of the mantle (well, it's a partial melt of the mantle), and a quartz pebble, kind of representative of the crust (because it is higher silica and should be less dense than basalt), but these are inexact and quite possibly confusing. So how about one silicate rock, and then the iron?

Thanks for writing an interesting activity! I hope you will do edits and post it publicly, and that you will continue to edit it over the year when you use it in your classroom.

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Hello Ashley -

I'll be interested to learn how kids go about the first part of the activity, and whether the groups come up with different ways of determining density. It seems that it will work well as an assessment opportunity for you, and that it could easily take the 45 minutes.

Since you want to link the activity to planetary differentiation, you could think about it using it later, after you have talked more about that process. You could ask kids to figure out which material would be likely to be found in the mantle, and which in the core.....

As for part 2, I'm remembering some variations on what you planned that were proposed in class. One (from Lindy?) was that kids could calculate the density of a planet that was half one material and half another. There were some other ideas, I think, aimed at giving kids enough information that they could carry out a calculation that would make sense. Maybe folks can add those to the discussion.....

Keep us posted as you move ahead with this!

Ellen

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