Hands-on Activity: Determining Densities
Educational Standards :
Pre-Req Knowledge (Return to Contents)
Learning Objectives (Return to Contents)
Materials List (Return to Contents)
Introduction/Motivation (Return to Contents)
The lesson Introduction, in which students determine the density of a rectangular box filled with an unknown substance, should provide adequate introduction to the activity. To further motivate students, explain that you have a variety of materials for which they can try to determine the densities. Mention that some of the materials have known densities, meaning that scientists have determined their densities to a high degree of accuracy, using sophisticated measuring devices. Tell the students that after they have determined the densities of the objects available, they can compare their results to the known densities. The challenge is for them to measure and weigh their objects very carefully, so they will be able to get results that are very close to the known densities.
Vocabulary/Definitions (Return to Contents)
Procedure (Return to Contents)
With students working in teams, ask them to determine the densities of the objects in the first assortment listed in the Materials section. Create a large data table on the board with room for each team to enter its results for each object, rounding densities to the nearest one-hundredth. Different teams should get slightly different densities for the same objects, and it would be good to have students discuss why these differences occur. (See Investigating Questions and Trouble Shooting Tips). If two teams get very different densities, however, it is likely that a measurement error was made, and the students involved should repeat their measurements and calculations.
Next, present the class with the second assortment of objects, whose shapes are not regular. Ask students to work within their groups to figure out a way to determine the densities of these oddly-shaped objects. Give them plenty of time to explore this problem (5-10 minutes, perhaps). If they can't come up with the water-displacement method on their own, ask them to imagine filling a bathtub all the way to the top. Then ask what would happen if they took a gallon jug of juice and lowered it into the water. How much water would spill over the edge of the tub? What if they lowered themselves into the filled tub of water until they were completely submerged -- how much water would spill out? Would it be possible to catch and measure the amount of water that spilled out?
Note: You will need to point out that liquid volumes are measured in liters or milliliters, but solid volumes are measured in meters or centimeters cubed. By a fortunate coincidence, however, 1 milliliter of water equals 1 cubic centimeter of water. (Students could also determine this for themselves.) This means that using standard laboratory graduated cylinders to measure displaced water allows for a very easy conversion of the volume of displaced water to the volume of the object. The volume in milliliters is simply the same as the volume in cubic centimeters, with the latter being the proper unit for density.
Make the beakers, graduated cylinders, trays, and funnels available to students so that they can devise their own water-displacement methods to determine the volumes of the oddly-shaped objects. If students have trouble devising an accurate method, offer suggestions, but let them do some problem solving on their own before stepping in. The idea is for students to place a beaker on the tray, and then use one of the other containers to fill the beaker with water to the point where it just begins to overflow. Students should then wait for any last overflow dripping to stop before placing an empty container at the beaker's spout to catch the soon-to-be displaced water. Students will likely discover that they need to lower the object into the beaker gently to avoid splashing, since splashed water will affect the amount of displaced water collected.
For the smaller objects, students may be able to simply submerge the object into a partially filled graduated cylinder. The change in water level will equal the volume of the submerged object. This method is more accurate than measuring water that has spilled out an overflowing beaker.
You may need to remind students of the need for accuracy, not only in the weighing of the objects, but also in measuring the volume of displaced water. Using the smallest graduated cylinder possible will allow for a more accurate measurement. Students should try to estimate the volume of water that will be displaced, and match the size of the graduated cylinder to the estimate.
You might also need to ask students which they should do first: find the mass of the object or find its volume. They should be able to reason that the objects will be weighed more accurately if they are weighed first, since that way they will be completely dry and no water will be added to the mass.
For any of the objects that float, students will have another problem to solve. They may try using a pencil point to hold the object just below the surface of the water. They could also use thread to tie the object to another, heavier object that will sink, such as a rock or piece of metal. They will then need to subtract the volume of the rock or metal from the displaced volume of water in order to obtain the volume of the otherwise floating object.
As in Part 1, create a large data table on the board with room for all teams to enter their results, rounding their densities to the nearest one-hundredth. Have any teams with widely disparate results repeat their measurements and calculations.
Use the table below to compare the student results to the known densities of the common materials shown. If the materials from which some of the objects were made are known, students can compare the accuracy of their determinations to the known values. If the materials the objects are comprised of are not known, students may be able to speculate about their composition based on the values in the table.
After students have determined the densities of the objects, ask them to find one more density, that of water. They may be puzzled at first, but give them time to realize that, just like the solid objects, they only need to find the mass of a known volume of water. (You may need to remind them to subtract the mass of the container for the water.) Check their results to make sure they get a density close to 1.00.
Next, have each student create a scatter graph for the objects, in which mass in grams is on the x-axis, and volume in cubic centimeters is on the y-axis. Their graphs should look something like the one below. Have students add the dashed line that forms the diagonal to their graphs. Explain that this represents the density of water, since for pure water, the mass in grams is equal to its volume in cubic centimeters. Put another way, the ratio of mass to volume is approximately 1 g/cm3 at room temperature and pressure, as long as the units are grams and cubic centimeters (cm3).
Have students examine their completed graphs. Ask students what the points that lie above the dashed line have in common. Although there may only be a few of them, students should note that these are the least dense of the objects and in fact, they are the objects that float. The points for all the other objects, the ones that sink, lie below the line. In other words, they are denser than water. Make sure students understand that, ordinarily, anything less dense than water floats, and anything more dense than water sinks. If students argue that ships are made of metal but float nevertheless, ask them why they think that is so. (This topic is explored in the lesson What Floats Your Boat?)
Troubleshooting Tips (Return to Contents)
Investigating Questions (Return to Contents)
Assessment (Return to Contents)
Activity Extensions (Return to Contents)
Other Related Information (Return to Contents)
This activity was originally published, in slightly modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit the website http://www.biology.duke.edu/cibl for information about CIBL and other resources for K-12 science and math teachers.
ContributorsMary R. Hebrank, Project Writer and Consultant , Duke University
Copyright© 2004 by Engineering K-Ph.D. Program, Pratt School of Engineering, Duke University
including copyrighted works from other educational institutions and/or U.S. government agencies; all rights reserved.
Supporting Program (Return to Contents)Engineering K-Ph.D. Program, Pratt School of Engineering, Duke University
Last Modified: March 7, 2014