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Density
Rubric
Contributed by: Council of Chief State School Officers (CCSSO)

Item Description:
The purpose of this event is to introduce students to the concept of buoyancy. In this experiment the students construct three boats of varying shapes out of three 15 centimeter square pieces of tinfoil. The boats are placed in a tub of water and washers are slowly added to them until they sink. Students are expected to understand the concept of, including the formula for, density. The density of a substance is its mass per unit of volume.

The principle of buoyancy states that a body (such as a boat) will float on a surface of water as long as the density of the body is less than the density of the volume of water displaced by the body. As stated in the question, the density of water is one gram per milliliter. So, in other words, as long as the body's density is less than 1g/ml, it will float.

In the first question, students are asked to calculate the density of one of the boats they made at the point that it sank and to show their work for the calculation. At the very least, students should show the formula for density (density=mass/volume) or show the division of mass by the volume of one of the boats. The students are then asked to compare the density they have calculated to that of water. Because there is a certain degree of experimental error involved with this event, the last part of question one asks, "When the boat sank, should the density of the boat and washers have been higher or lower than the density of water?" The answer, of course, is higher.

NOTE: The experimental error involved can occur because the boats can be constructed improperly so that they sink before their density reaches 1 g/ml or tip over. In fact, there was a wide range of results to this experiment. Also, the volume of the boats may be only approximately calculated by the simplified formula given for volume: length x width x height.

Question number two poses a hypothetical situation in which two boats have been created one with a volume of 500 cubic cm and another with a volume of 400 cubic cm. "Which of these boats will be able to support more mass before sinking?" The correct answer is Boat 1 - the boat with the volume of 500 cubic cm. Because density is inversely proportional to volume, a boat with a greater volume will be able to support more mass than a boat with less volume.


The Item:
Question #1: Calculate the density for one of the boats you made, including the mass of the washers that made the boat sink. Show your work. Compare the density you calculated for the boat and washers to the density of water. (The density of water is 1 gram/ml). When the boat sank, should the density of the boat and washers have been higher or lower than the density of water? Explain your answer.

Question #2: Suppose that your lab partner creates two boats from two identical pieces of aluminum foil. The volume of Boat 1 is 500 cubic cm. The volume of Boat 2 is 400 cubic cm. Which of these boats will be able to support more mass before sinking? Explain your answer.


ME127 Rubric

Criterion 1: In question one, score one point for a correct calculation of the density of one of the boats. Students should show their work, especially the formula for density.
Criterion 2: In question one, score one point if the student states that the density of the boat and washers should have been higher than the density of water when the boat sank.
Criterion 3: In question two, score one point for identifying Boat 1, the boat with the volume of 500 cubic cm, as the boat that will support more mass before sinking.
Criterion 4: In question two, score one point for correctly explaining that it is the larger volume of a boat that allows it to support more mass. A student must use the word "volume" in their answer to get this point. "Bigger", "more area", "because the walls are higher" are insufficient explanations of the underlying conceptual understanding that students should have made: that increasing the volume of a boat allows it to support more weight.

 


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