Density Curriculum

Section 3—Lesson 11: What Does it Mean for Density to Have Multiple Contributing Causes?

Lesson Plan

Materials

Prep Step

Review, Extend, Apply

Step 1: Group Discussion: What Causes Density in Particular Examples?

As a group, discuss each of the following objects/substances in terms of what contributes to their density: 1) a piece of copper; 2) a piece of bread; 3) steam in the air. The sheet, Group Discussion of the Causes of Density is provided in case you want students to draw and think along with the class. For instance, for the copper, because you have a pure, solid metal sample, such as is describe by the first two causes, the mass of the atoms and the structure of the bonds account for the density of the object. But the bread and the steam in the air provide examples of mixed densities, and therefore you must consider Cause #3. Discuss how scientists might picture the various objects inside. Invite the students to contribute to the drawings and to discuss and critique them.

Going through the sample substances one at a time, ask students which causes they think contribute to the density of each object. For each substance, ask:

  • Do you think the first cause, the mass of the atoms, explains its density? In what way does Cause #1 help or not help to explain the density? How can you illustrate this in their drawing? (If you haven't already, generate some group conventions for illustrating the concept.)
  • Does the second cause, the structure and strength of the bonds, explain its density? In what way does it help explain the density? How can you show the bonds? (If you haven't already, generate some group conventions for illustrating the concept.)
  • Does the third cause, mixed density, explain its density? That is, is this a pure substance, or is there more than one substance in the object that you must consider? (Again, consider as a group how you will show it.)

Explore Causality

Step 2: What Does it Mean to have Multiple Causes?

Have the students read the sheet Multiple Causes. Explain that when there are multiple contributing causes, you need to consider the different possibilities involved and whether each is involved in explaining different cases. The explanation page uses social examples to explain necessary and sufficient multiple causes.

Discuss the social examples with the students. Then go over the back of the sheet together and discuss multiple causes and density. Make sure the students understand the examples that are given.

Explain why there are quotation marks around the word "density" in reference to the helium atom. The only possible contributor to density that one atom can have is atomic mass.

Review, Extend, Apply

Step 3: Drawing Models of Multiple Causes of Density

Pass out the sheet, What Causes Differences in Density?: Drawing Models. Show the students the following examples: 1) a cylinder of steel; 2) a piece of steel wool; 3) a piece of Styrofoam; and; 4) picture of a soap bubble. Have students analyze each example as you did in Step 1 with the copper, bread, and steam. Have them draw a model of each. In each case, they should consider which cause or causes might be involved and illustrate it (or them). For instance, for the steel, the first two causes, the mass of the atoms and the structure of the bonds, both account for the density of the object. But objects #2, #3 and #4 provide examples of mixed densities, and you must consider the third cause as well.

Explain to students that they should take their best guess at what causes each object's density. They won't know for sure, though there are answers that are better reasoned than others and there are causes that they can rule out in some instances. Remind the students of how some causes might matter in a specific case while others won't, and remind them of the examples that you showed the class. You may wish to hand out the sheet, Thinking About Multiple Causes for the students to refer to.

After the students have had a chance to analyze each model, discuss the examples together. Help them to see instances where they have not thought about the contributions of one of the causes. Draw students' attention to different cases where one cause is in play, or two, or even three.

Step 4: Reasoning about Multiple Causes and Density in General

Hand out the sheet, Pitfalls in Reasoning About Density and have students find the reasoning pitfalls in each paragraph. This activity can serve as an informal assessment of students' understanding if it is completed individually instead of in pairs or groups.