Density Curriculum

Section 2—Lesson 5: Why Is Density Considered a Property of a Particular Kind of Matter?

Lesson Plan

Materials

Prep Step

Analyze Thinking

Step 1: Why is Density Considered a Property of a Particular Kind of Material?

Ask the students to think of examples of properties of materials (such as color, hardness, texture, odor, break-ability, boiling point, melting point), as opposed to properties of objects (such as size and shape). Generate a list of examples on the board. Ask, "Does it make sense that density is a property of a certain kind of material? Why or why not?"

Step 2: Does Cutting an Object in Half Affect its Density?

Students may be aware that the size and shape of an object does not affect its density from the activity in Lesson 3. However, many students are still unclear on this point. As a reinforcement activity, have the students work in small groups. Give each group a long cylinder of Styrofoam. Ask each group to think about what would happen if you only had half of the cylinder. Would the density change or not? Make sure that students first calculate the density of the entire cylinder.

Explore Outcomes

Step 3: Testing Predictions

Have each group discuss their predictions and how they would test them. They should explain not only whether they think the density would change or not but how. Students who think that the density would change typically predict that it will be half. Then have students test the density of the Styrofoam cylinders by using the catch pans, graduated cylinders, balance, and gram masses.

After the students have calculated the density for the whole object and for half of it, discuss their findings. They should find that the density is approximately the same. There will be very slight variations because Styrofoam is actually a mixed density of Styrene plus air. However, they will find that the density is certainly not half of what it was for the whole cylinder. For now, you can talk about the slight variations as due to measurement variations. After Lesson 10 where students learn about mixed density, you can come back to this activity as an example.

Next, pose the question, "What if I kept cutting this in half until I had a very tiny fragment? What would happen to the density?" Show the students a very tiny piece of the Styrofoam. Have them discuss their ideas in their groups and find a way to show what the outcome could be. Circulate while they are working and encourage them to use various models (Particle, Dot-Per-Box, or other models) and to demonstrate it mathematically. Some students may want to actually try their ideas. What kinds of difficulties do they think they might run into?

Explore Causality

Step 4: Why is it Hard to Realize That Density Doesn't Change with Size or Shape?

Ask students to think about how volume, mass and weight can be measured, and point out that different sized pieces of the same kind of material will have different volumes and masses. Compare this to the density of a pure substance, which is the same no matter what size the piece is (at stable pressure and temperature). The density is not affected by the size or shape of the object.

While it is possible to logically reason that taking half of the cylinder again and again until you have a tiny fragment would result in a piece with the same density, this is still counterintuitive for most of us. Ask the students, " Why do you think it is hard for people to realize that cutting the cylinder in half does not change its density?" Gather their ideas.

There are at least two reasons that have to do with how we reason about causality:

  • One has to do with Relational Causality. It is hard to focus on the relationship of mass to volume, which stays the same. It is generally harder to hold two things in your mind and think about the relationship between them then it is to just focus on one variable.
  • The other has to do with the non-obviousness of density. It is much easier to focus on the more obvious features of weight and size. After all, you can see and feel those!

Review, Extend, Apply

Step 5: Introducing the Densities of Common Substances

Put up the overhead of the Densities of Common Substances Under Standard Conditions Table. Explain that scientists assign certain numbers to the densities of different substances. Each substance has its own number. In order to get these numbers, scientists test the substances under standard conditions. This means that they keep the temperature and the amount of pressure the same. Explain to the students that they will revisit this concept a little later in the module.

Step 6: Making Connections: "The Case of the Missing Crown"

Pass out the sheet entitled, Archimedes and the Golden Crown. Have students read it and answer the question. The sheet asks them to make the connection between a certain substance having a certain density and the ability to identify that substance.

Invite students to share their solutions with the class. Try to get a sampling of different kinds of responses. Tell the students to compare the different solutions that they came up with and think about which they think would work the best.

Guide the inquiry by asking questions that get to the issues in the story and support the following understandings:

  • Density is a property of a certain kind of material.
  • We find the density by measuring the relationship between the mass and the volume of an object made of that material.
  • Comparing the density of the material a crown is made of to the density of gold will tell us what kind of material the crown is made of. The density of gold can be found by finding the relationship between the mass and volume of a known piece of gold.