Density Curriculum

Section 4—Lesson 15: What Happens in Sinking or Floating When the Relationship Between Densities Changes?

Lesson Plan

Materials

Prep Step

Analyze Thinking

Step 1: How Can We Manipulate the Relationship Between Densities?

Ask the students to think about the relationship between two densities. What are some ways that we can change the outcome in any given case?

Encourage the students to see that we can change the density of a substance to a certain extent, but that once we change the direction of the differential, the outcome tips the other way. It is an example of a kind of "tipping point" phenomenon. There are some events that we don't notice until they reach a certain threshold or point. Encourage them to think of supporting examples.

RECAST Thinking

Step 2: RECAST Activity: Which Pop Rises to the Top?

Do the following demonstration for the class. Show the students unopened cans of diet and regular soda. Ask how they can tell what is different and what is similar between the two cans. Write their responses on the board. If none of the students mention that the volumes are equal, ask them directly what they think about the volumes. (Optional: If the students want to weigh the cans, weigh them on the electronic scale or triple beam balance.)

Pass out the sheet, Diet Versus Regular Soda: Which Pop Rises to the Top?. Ask students to answer the first question, which asks them to predict what will happen when the diet and regular soda cans are placed in water.

Next, fully immerse the can of regular soda in water (it should sink and stay sunk), and then immerse the can of diet soda (it should rise to the surface and float). Have students make observations about what happened.

Soda Can demonstration

Then have them compare their observations with their predictions. Ask students to offer probable explanations for their observations. If no one suggests that they read the list of ingredients on the side of each can, suggest that they do. Ask the students:

  • Does the volume of the sodas vary? [No, because they are both in 12 oz cans.]
  • Do the different solutions contain anything that might make them more or less dense? Discuss responses. [Regular soft drinks are sweetened with dissolved sugar and/or high fructose corn syrup. A great quantity of this relatively dense substance is needed to sweeten regular soft drinks. The artificial sweeteners in diet drinks are many times sweeter than sugar and so they are required in smaller quantities. Therefore, although the volume of the cans is the same, the masses are different due to the sweetener.]

Ask the students how the densities of the regular and diet soda cans compare to the density of the water, which is 1g/ml. Ask the students to answer questions 2 to 4 on their sheet.

Discuss their responses.

Ask the students to predict the following: "What do you think will happen when we add corn syrup to the water? Why?" Add corn syrup to the water slowly, being sure to mix it thoroughly with the water until the regular soda can floats.

Then pose the following question, "What happened in terms of the relationship between the water and the can of regular soda? Why?" Collect their ideas.

[The addition of corn syrup to the water created a mixture that had a density greater than 1 g/ml, the density of water alone. Since the regular soda can floated to the top of the container, the density of the can in relation to the new mixture must have changed. The regular soda can is less dense than the corn syrup/water mixture, and this new relationship caused the can to float. When thinking in terms of sinking and floating, we must not only consider the density of the object being sunk or floated, but the density of the liquid the object is immersed in as well. We also need to consider how possible changes might impact the relationship.]

Explore Causality

Step 3: Thinking About the Cans of Soda Using Relational Causality

Draw the diagram for Relational Causality on the board to analyze what happened. When determining whether or not an event is best described by Relational Causality, ask yourself:

  • In Relational Causality, there is more than one "thing " in the model. Is there more than one "thing" in this model? What are the things?
  • In Relational Causality, it is the relationship between the two things that accounts for the outcome. Look for balance or differences in amount and what happens in the different cases (the things are equal to each other, or one is more than the other). Does the relationship between them (how much you have of one compared to how much you have of the other) cause the outcome?

Review, Extend, Apply

Step 4: Analyzing an Analogy

Galileo's thermometer

Show the students the Galileo's thermometer. How do they think it works? Turn on a heat source near the thermometer. What do they notice? What is going on and why? Ask the students to compare the Galileo's thermometer to the activity with the soda cans. Pass out the sheet called Analyzing an Analogy: Galileo's Thermometer. Using diagrams and written explanation, the students should show how it is similar and how it is different to the soda can experiment. Their explanations should not be at the surface level (i.e. "one is a tube, one is a vase") but at the deep, structural level (i.e. "they both have to do with density in the following ways...").

Step 5: Making Connections With Density

Ask students, what are some ways that humans and animals manipulate density to their advantage? Pass out the sheet, Making Connections with Density. Ask the students to answer the questions on the sheet using outside information sources to help them. The questions are designed to help students make connections and to apply what they have learned about the Relational Causality involved in sinking and floating to problems in the real world.