Density Curriculum

Section 3—Lesson 10: How Does Mixed Density Contribute to Overall Density?

Lesson Plan

Materials

• Cause #1, Cause #2, and Cause #3 posters (PDFs)
• 10 ml graduated cylinder, 1 per group of 3-4 students
• Catch basins, 1 per group of 3-4 students
• Triple-beam balances, 1 per group of 3-4 students
• Assorted materials and objects:
  • clay
  • balsa wood pieces of various shapes
  • corks of various shapes
  • Styrofoam pieces of various shapes
  • other every day objects or materials

Prep Step

• Review the lesson plan, background information, and understanding goals.
• Gather materials.
• Enlarge the Cause #3 poster to post beside the Cause #1 and Cause #2 posters.

Analyze Thinking

Step 1: What Else Causes Differences in Density?

Explain that in this lesson, you will be considering another cause of differences in density. Based on what the students have already learned, can any of them guess what it is?

So far you have explained causes of density that do not involve air. This last cause can include air.

Explore Causality

Step 2: Introducing Mixed Density

Put up the Cause #3 poster next to the posters from the previous lessons. Explain that the third cause is a little less "zoomed in" than the first two causes. This cause is most easily talked about as mixed density. One example is when a gas, such as water molecules in the form of steam, spreads out in a room and there are lots of "air molecules" in between the "water molecules." Other examples include a sponge with holes in it. The state of the molecules affects how spread out they are. For instance, Styrofoam is formed by blowing air into a dense liquid, Styrene. The air greatly increases the liquid's volume without adding much mass, and the density of the resulting Styrofoam is due to the combination of the density of the Styrene and the density of the air. The in-between space in this case is air (sometimes it is another material instead).

Explore the idea of mixed density with students. Consider the examples on the chart. Then ask, "How does mixed density explain a hollow object?" Gather ideas. [Students have to account for the density of the surrounding material and the density of the air inside.]

Note to Teacher: Depending upon the class, you might tell your students as an aside that you have simplified the third cause a little to make it easier to understand. It is basically correct. It leaves out some special cases, for example, certain kinds of plastics.

Explore Outcomes

Step 3: Exploring How Mixed Density Affects Overall Density

This activity invites the students to experiment with different mixed densities by combining materials to create a composition of a given density.

Divide the class into groups of 3-4 students. Give each group an assortment (or access to a class collection) of materials and objects. First, the students should choose a target density range. They can look on the density chart from Lesson 8 to choose a target. They shouldn't choose densities in the range of the heaviest or lightest elements. Ask them to explain why not. Then they should work on assembling an object with this density, pausing periodically to measure its mass and volume and to calculate its density.

While students are working, circulate to discuss how students are approaching the task. You can use this as an assessment of how they apply what they know about density and how much they plan out their approach.

Afterwards, ask the students to share both what they did and how they approached the task.

Review, Extend, Apply

Step 4: Critiquing the Models from Lesson Two: What They Reveal About the Causes of Density

Step back to re-consider the models that were presented in Lesson 2. What does each help to show in terms of the three causes of density? Engage the students in a discussion of each model. Discuss the models by asking others what makes sense about a particular model and what doesn't. What could we do to improve the model? What do the models share that help us understand density better? Try to draw out the following points:

Bread Model

• It shows how something takes up a certain amount of space (volume) and has a certain mass. When you squish the bread, you have a different volume but the same mass; therefore, you must have a different density.
• It shows how the same number of particles packed into less space means greater density.
• It models mixed density, until you squish the air out. After the air is gone, it is no longer a mixed density.
• It is not a good model of the cylinders unless you think of the air holes as standing for the spaces in between the particles.

Wooden Balls and Marbles Model

• This model controls for volume, but lets students feel and measure differences in mass, so it shows that things can have the same volume and different masses due to density.
• We can think of the balls as atoms.
• It offers a way to think about the atomic mass of different atoms being different.
• It doesn't capture the idea of the structure and spacing of atomic bonds.
• In order to represent atoms, the balls should be exactly the same size so that it doesn't make it seem like particle size accounts for density differences.

Dots-Per-Box Model

• This model shows different amounts of dots that could represent atoms and correspond to different atomic masses. (You would have to imagine this.)
• It captures the concept of atomic bonds in some respects by showing how far apart or close together particles are.
• You could use it to show the differences in a mixed density object by showing different numbers of dots per unit space.

Step 5: Making Connections

As a class, generate a list of all of the examples of mixed density that you can think of. Some examples should come from previous discussions, like a beach ball or Styrofoam. What others can the students think of? Try to make your brainstorm open-ended, such that students are encouraged to put any possible example out and then to discuss it. Try to make your list broad so that it includes many different kinds of examples.