### Summary

Students are introduced to the important concept of density. The focus is on the more easily understood densities of solids, but students can also explore the densities of liquids and gases. Students devise methods to determine the densities of solid objects, including the method of water displacement to determine volumes of irregularly-shaped objects. By comparing densities of various solids to the density of water, and by considering the behavior of different solids when placed in water, students conclude that ordinarily, objects with densities greater than water sink, while those with densities less than water float. Density is an important material property for engineers to understand.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Density is an important property in many materials engineering applications. Students use engineering in this unit by designing boats to float with various amounts of weight.

### Pre-Req Knowledge

Students should be able to use rulers to measure lengths to the nearest millimeter, and triple beam balances to measure masses to at least the nearest 0.1 gram.

Students should know how to calculate the volume of a rectangular prism (such as a box).

### Learning Objectives

- Students will be able to define density as the amount of mass per volume a material contains.
- Students will be able to calculate the densities of objects when given their masses and volumes.
- Students will be able to compare the densities of several common materials.
- Students will be able to explain that materials that are denser than water ordinarily sink, while those less dense than water will float.

### More Curriculum Like This

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###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Modeling, testing, evaluating, and modifying are used to transform ideas into practical solutions. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### North Carolina - Math

- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### North Carolina - Science

- Compare the physical properties of pure substances that are independent of the amount of matter present including density, melting point, boiling point, and solubility to properties that are dependent on the amount of matter present to include volume, mass and weight. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand the structure, classifications and physical properties of matter. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?

### Introduction/Motivation

Density is an important concept, and one that has a wide variety of applications in science and technology. The relative densities of solids can be a very important consideration in engineering design, with the choice of aluminum over steel for the construction of airplanes being an obvious example. Densities of liquids and gases are no less important. Without an understanding of how density affects the behavior of gases and liquids, our understanding of weather conditions and ocean currents would be minimal at best – yet both of these determine global climate patterns, and will continue to have far reaching effects on human populations as our current trend toward global warming continues.

In this lesson, students are first led to the idea of density as a way to compare materials based on how much "stuff" (matter, mass) is packed into a certain volume. Start by showing the class three or four boxes that appear to be identical, for example, diskette boxes, or boxes that once held macaroni and cheese dinners. Each box, however, should now be filled to the top with a different material. One box might contain uncooked rice or uncooked popcorn, another dry cereal or popped popcorn, a third M&M's™ or other candy, and the last pebbles or small rocks. (These are just examples -- other substances will do, as long as they represent a range of masses for the given volume of the boxes.) Let students handle the boxes, but do not let them open the boxes. It would be a good idea to tape them shut, anyway, to prevent leaks. Then ask the class to compare the features of the four boxes, writing their observations on the board.

They should note that the boxes look identical, so be sure they refine this observation to include the idea that their volumes are identical. They should also note that the boxes had different weights, or masses. Once these two observations have been made, you can let students know there is one word that includes both of those observations. That word is density. Density tells us how much material is packed into a given amount of space. It tells us how the masses of two different objects would compare if they both had the exact same volume.

The dry cereal (or popped popcorn) is not very dense. The material in the box does not weigh very much, because there is a lot of air occupying the spaces between the cereal flakes (or between the popped corn kernels, which themselves contain a lot of air, too). The candy and rice grains are more dense; they can pack together more tightly in the box. Sand grains can pack very tightly together, and so the box containing them is the densest of all.

Once students understand the idea of density, ask them how it could be quantified. Point out that we use meters for describing length, degrees for describing temperature, and miles per hour for describing speed. What units should we use for describing density, if it is the amount of material that fits into a given volume? Give them a few minutes to grapple with this problem, and they should be able to identify mass (or weight) and volume as the quantities needed. They may have more trouble realizing that mass needs to be divided by volume, however. Density is defined as the amount of mass per volume of a substance, and it may help to tell students that per always means divide. (They are probably already familiar with speed: to find the speed, they divide the miles traveled by the hours it took to travel them. This division results in the speed expressed as miles per hour.)

Divide the class into teams of 3-4 students each, and give each team of students one of the boxes. (Depending on class and team size, you may need some duplicate boxes.) Ask each team to determine the density of its box. Again, let them figure out that they will need to find the mass of the box, as well as measure its dimensions to calculate the volume. Once they have arrived at a method, provide rulers and triple beam balances for them to use. As students begin to measure the boxes, tell them to make their measurements in centimeters, so their volumes will be given in cubic centimeters. Once they have made their calculations, write the densities (including the units, g/cm3) on the board. Have students check to make sure their answers make sense (the heavier boxes should, of course, have higher densities.)

Once students are able to determine the densities of the boxes, they are ready to complete the associated activity, Determining Densities.

### Lesson Background and Concepts for Teachers

Density is defined as the amount of mass per volume a substance contains, and it is normally expressed in units of g/cm3 or kg/m3. Densities can be determined for solids, liquids, and gases. Generally, solids are the most dense, then liquids, and gases have the lowest densities. These differences are mainly the result of the spacing between the molecules comprising the substances. In solids, molecules are packed very tightly together, while in gases, there is much more space between adjacent molecules. There are exceptions, of course. Mercury is a very dense metal that occurs as a liquid at room temperature, and although it is a liquid, it is nearly twice as dense as steel and about five times as dense as aluminum. On the other hand, plastic foams (such as Styrofoam™), contain many air pockets and although they are solids, they are usually less dense than water.

Densities can be affected by temperature. When heat is applied, the kinetic energy of the molecules increases and they bounce more forcefully off one another, increasing the distances between molecules and thus lowering their overall density. This density difference is most easily observed in water. On a hot summer day, the surface waters of a lake will be quite warm, but diving down below the surface reveals much cooler water at lower depths. Because the cooler water is more dense, it remains deep in the lake, while the less dense, sun-warmed water remains at the surface.

Similarly, when water is heated in a pot on a stove, it can become hot enough to boil. At that point, the density of the water decreases so much that the molecules can no longer stay in liquid form, and the water becomes a gas. We can see this as steam rising (because it is less dense) above the boiling water. If those steam molecules come in contact with a cool surface, however, they quickly lose some of their heat and condense back into more dense water droplets.

It is not necessary for middle-school students to be taught about the effects of temperature on density in this lesson, however. This information is provided because the complete definition of density is the mass per unit volume of a substance at a given pressure and temperature. When densities of common substances are listed in reference materials, the densities listed are usually those that occur at room temperature (about 20° C) and standard pressure (atmospheric pressure at sea level).

### Vocabulary/Definitions

density: The mass per unit volume of a substance at a given pressure and temperature.

### Associated Activities

- Determining Densities - Students devise two different methods to determine the densities of a variety of materials and objects, some of which have simple geometric shapes, and some of which are irregularly-shaped.

### Lesson Closure

Hold a brief discussion in which students are asked what the main points of the lesson were. They should be able to define density and explain why it is a useful concept: since the weight of an object or material can vary with the size of the object, if we want to compare how heavy different materials are, we use density because that eliminates the effects of size. Students should also be able to compare densities of common materials, for example, metals are more dense than wood and plastic. Furthermore, students should be able to recognize that objects that are less dense than water will float in it. The next lesson (What Floats Your Boat?) explores the concept of buoyancy.

### Assessment

- Provide students with a table of densities of common materials. Ask them to identify the material with the highest density, and the material with the lowest density. Ask them to give an example of a material that will float in water, and a material that will sink in water. Also, ask them what the density of water is.
- Provide students with a list of several objects, their masses, and their volumes. Ask students to calculate the density for each object, and check that they include units in their answers.

### Lesson Extension Activities

Use the material in the Lesson Background section to lead a discussion about the effects of temperature on density. Begin this discussion by asking students if they've ever swum in a lake or the ocean and noticed the difference between the water temperatures of the surface versus bottom waters. Or, ask if they know why steam forms above a pot of boiling water. From your questions, expect students to establish that for the same material, solids are denser than liquids, and liquids are denser than gases. Furthermore, colder liquids or gases are denser than warmer ones. Have students model what happens to the density of a material when thermal energy (that is, heat) is added. Students should represent the material, which we'll say is a liquid, as a collection of particles. Have students draw evenly spaced particles over some area of their paper, count the number of particles, and estimate the average distance between particles. (Alternatively they could use dots or something physical to represent the particles, and spread the particles over some space, like their desks.) Now, tell the students that thermal energy will be added to this system, and ask them to show what happens to the particles, by drawing their system at a higher energy state. Prompt students by asking, "Do the number of particles increase when thermal energy is added? What about the volume of space that the particles occupy?" Students should understand that the mass of the system is not changing when heat is added, but the same mass is occupying a larger space. Their physical models should help them grasp the concept.

Then, once students understand how thermal energy affects density, ask them whether ice floats or sinks in water. They should quickly realize that ice floats, but this doesn't make sense! Since it's the solid form of water, it should be more dense and thus sink. Provide students with some ice cubes (as large and rectangular in shape as possible), and have them determine their densities, just as they did for the other solid objects. They should indeed find that ice is less dense than water.

This is one of the unique properties of water: it is the only natural substance for which the solid form is less dense than the liquid form. It's a good thing, too. The layer of ice that floats on the surface acts to insulate the rest of the water below, keeping it from freezing solid, and thus preventing fish, plants, and all the invertebrate and microbial lake-dwellers from also freezing solid and dying as soon as the temperature gets below freezing. Also, since it prevents a body of water from freezing solid, it allows people living in cold climates to be able to obtain drinking water easily, without having to melt ice, during the winter months.

### Contributors

Mary R. Hebrank, project writer and consultant### Copyright

© 2013 by Regents of the University of Colorado; original © 2004 Duke University### Supporting Program

Engineering K-PhD Program, Pratt School of Engineering, Duke University### Acknowledgements

This content was developed by the MUSIC (Math Understanding through Science Integrated with Curriculum) Program in the Pratt School of Engineering at Duke University under National Science Foundation GK-12 grant no. DGE 0338262. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

This lesson and its associated activity was originally published, in slightly modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit http://www.biology.duke.edu/cibl for information about CIBL and other resources for K-12 science and math teachers.

Last modified: April 10, 2018

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