This is the fourth Investigation of the LabLearner CELL Density. In this Investigation, students determined the densities of several different solids.  They used both mathematic formulas and volume displacement methods to determine volume.

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A. Begin analysis of this Investigation by encouraging students to summarize the experiments they conducted in the lab and the purpose of those experiments.  Pose the following questions to prompt student discussion:

1. Ask students: What were the main questions we wanted to investigate in this lab? The main questions Investigated in this lab were:  Can the density of all solid objects be measured using the formula for measuring volume?  Can the density of all solid objects be measured using the volume displacement method?  Does changing the size of a solid change the density of that solid?

2. Ask students: How would you summarize the types of experiments that you performed to investigate these questions? Students tested the density of five solid objects using two methods.  The first method, the formula for measuring volume, required students to calculate the volume of each object using one of the following formulas:  volume = length × width × height or volume of a sphere = 4.2 × radius × radius × radius.  Students then used the triple beam balance to measure the mass of each object.  The values for volume and mass were applied to the equation, density = mass ÷ volume.  The second method, the volume displacement method, required students to measure the volume of each object by individually dropping each object into 500 ml of water.  The volume of the object was equal to the change in the volume of the water.  The values for volume and mass were applied to the equation, density = mass ÷ volume.

B. Begin analysis of the lab by directing students’ attention to the results of Trial 1.

1. Ask students:  Could you use the formula for measuring volume to calculate the density of the metal cube?  What was the density of the metal cube?  Students may wish to refer back to Problem 3 to answer these questions. 

Students should indicate that the formula for measuring volume could be used to calculate the density of the metal cube.  Using the formula for volume, the metal cube was found to have a density of 7.13 g/cm³.

2. Ask students:  Could you use the volume displacement method to calculate the density of the metal cube?  What was the density of the metal cube?  Students may wish to refer back to Problem 3 to answer these questions. 

Students should indicate that the volume displacement method could be used to calculate the density of the metal cube.  Using the volume displacement method, the metal cube was found to have a density of 7.13 g/ml.

3. Ask students: Was one method better than the other for calculating the density of the metal cube? Students should indicate that both methods calculated a density of 7.13 g/cm3 or 7.13 g/ml for the metal cube.  Therefore, either method produced an accurate measurement of density.

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C. Ask students to recall Trials 2 and 3.

1. Ask students:  Using the formula for volume, what density did you calculate for the woodblock?  Students may wish to refer back to Problem 4 to answer this question. 

Students should indicate that the density that they calculated for the wood block was 0.71 g/cm3.

2. Ask students:  Using the volume displacement method, what density did you calculate for the woodblock?  Students may wish to refer back to Problem 4 to answer this question.

Student answers may vary.  A sample answer includes:  The density calculated for the wood block was 1.06 g/cm³.

3. Ask students:  Did you calculate the same density using both methods?  Which method do you think was better for accurately calculating the density of the woodblock?  Why? Students should indicate that they did not calculate the same density using both methods.  Students should also indicate that the formula for volume calculates a more accurate density for the woodblock.  The volume displacement method resulted in a lower volume than the measurement method of determining volume because the woodblock floated in the water.

Note to Teacher:  It should be noted that neither density calculated for the woodblock is the correct density of the woodblock.  The air in the wood decreases the mass which makes both density measurements incorrect.  The air decreases the volume when it is measured by the volume displacement method resulting in an incorrect density.  For the purposes of this experiment, the density calculated with the formula for volume provides sufficient accuracy for the calculation of density. 

4. Ask students:  Using the formula for volume, what density did you calculate for the pitchstone?  Students may wish to refer back to Problem 5 to answer this question. 

Student answers may vary.  A sample answer includes:  The density calculated for the pitchstone was 1.51 g/cm³.

5. Ask students:  Using the volume displacement method, what density did you calculate for the pitchstone?  Students may wish to refer back to Problem 5 to answer this question.

Students should indicate that the density that they calculated for the pitchstone was 2.16 g/ml.

6. Ask students:  Did you calculate the same density using both methods? Which method do you think was better for accurately calculating the density of the pitchstone?  Why? Students should indicate that they did not calculate the same density using both methods.  Students should also indicate that the volume displacement method calculates a more accurate density for the pitchstone. The formula for volume is not accurate because the pitchstone has irregular sides. It is difficult to accurately measure a length, width, and height.

7. Encourage students to summarize their findings from Trials 1-3 by completing the Table and answering the questions in Problem 7 of their Student Data Record.  Allow sufficient time for students to complete the Table and questions.  Review student answers.

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D. Continue the discussion of densities of different solids by encouraging students to consider what they learned from Trial 4.

1. Ask students:  Could you use the formula for measuring volume to calculate the density of the clay balls?  Students may wish to refer back to Problem 6 to answer this question.

Students should indicate that in order to calculate the volume of the clay balls they had to use the formula, volume = 4.2 × radius × radius × radius.  It should be noted that this formula calculates the volume of a perfect sphere.  If the student’s clay balls are not perfect spheres, the calculated volume may be slightly skewed.

2. Ask students:  Could you use the volume displacement method to calculate the density of the clay balls?  Students may wish to refer back to Problem 6 to answer this question.

Students should indicate that the clay balls sank to the bottom of the graduated cylinder, therefore, they were able to use the volume displacement method to calculate density.

3. Ask students:  Was one method better than the other for calculating the density of the clay balls? Student answers may vary.  Students should indicate that both methods calculated similar densities of the two clay balls.  Therefore, both are appropriate to use.

4. Ask students:  What was the volume of the first clay ball?  The second clay ball? Student answers may vary.  Students should indicate that the first clay ball had a volume of approximately 14 ml and the second clay ball had a volume of approximately 64 ml.

5. Ask students:  What was the density of the first clay ball?  The second clay ball? Student answers may vary.  Students should indicate that the density of the first clay ball was approximately 1.4 g/ml (g/cm³).  The density of the second clay ball was approximately 1.4 g/ml (g/cm³).

6. Ask students:  Did the density of the clay change as the size of the sample was changed? Students should indicate that the density of clay stayed constant as the size of the sample changed.

7. Ask students:  Imagine cutting the metal cube in half.  Do you think the density of the metal cube would change? Student answers may vary.  Encourage students to realize that, as with the clay balls, changing the volume or size of the metal cube will not changed its density.  That is, the density of solids is a constant.

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E. Begin a discussion of how to compare the densities of the solid objects explored in Lab.

Note to Teacher: In order for students to compare the densities of the solid objects explored in the lab, they should each compile all of their data onto a Table.  Then a comparison can be made. 

Model the use of the Compare Results tool, by thinking out loud.  First, state that your goal is to compare the densities of the solids tested in the Lab.  Then, state that in order to do this, you need all the results in one location on the Student Data Record.  This will allow a comparison.  Model thinking of a Table to do this and that after the table is completed, you will look at each solid in relation to every other solid.  Invite students to do this with you.

1. Divide the students into groups of three.

2. Instruct students to work together to complete the table in Problem 8a of their Student Data Record.  Tell students that when completing the table, they should use the most accurately calculated density for each solid tested in the lab.

3. Allow students sufficient time to complete the table.

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4. Ask student groups:  How could you present the data collected in the lab to show the difference in the density of each solid object? Student answers may vary. Allow several student groups to give suggestions.  After receiving suggestions, direct students to look at Problem 8b of their Student Data Record. Discuss the placement of students’ results along the horizontal line in Problem 8b as a way in which students could represent the results of their experiments.

5. Ask students:  How does the density of the metal cube compare to the density of the other solid objects?  The woodblock?  The pitchstone?  The clay balls? Encourage students to record their answers along the line in Problem 8b of their Student Data Record.  

The densities of the solids from least dense to most dense are as follows:  woodblock, clay, pitchstone, and metal cube.

6. Ask student groups to draw conclusions about their experiments by answering the following questions in Problem 8c of their Student Data Record:

a. Ask students: Do all solid objects have the same density? Students should indicate that all solid objects do not have the same density.

b. Ask students: Can the density of all solid objects be calculated using the formula for measuring volume?  Use data to support your answer. Students should indicate that the density of all solid objects can not be calculated using the formula for measuring volume.  In Trial 3, students were unable to calculate the density of the pitchstone using the formula for volume because it had irregular sides.

c. Can the density of all solid objects be calculated using the volume displacement method? Use data to support your answer. Students should indicate that the density of all solid objects can not be calculated using the volume displacement method. In Trial 2, students were unable to calculate the density of the woodblock using the volume displacement method because it floated.

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F. Remind students that in Problem 1 of the PreLab, they were asked to predict what the particle diagrams for solids, liquids, and gases looked like.

1. Ask students:  Can you recall some of the characteristics of gases?  Liquids? Solids? Students should indicate that gases are light, transparent, and weightless.  Liquids are wet, runny, can be poured, and do not have a definite shape.  Solids are hard and have a definite shape.

2. Ask students:  After performing this experiment, can you make any comparisons between the density of liquids and the density of solids? Student answers may vary.  Based upon this experiment, students should indicate that most of the solids tested were more dense than water.  That is, they sank into the water. Therefore, students may or may not make the conclusion that most solids are more dense than most liquids.

3. Ask students:  Do you think that gases are more or less dense than liquids and gases? Student answers may vary.  Encourage students to realize that gases are less dense than solids or liquids. If students are having difficulty with the concept, ask them to think about swimming in a swimming pool.  When they are under the water and exhale, gas (carbon dioxide) is released into the water.  The gas forms a bubble and floats to the surface of the swimming pool.  Therefore, the gas (carbon dioxide) is less dense than the liquid (water).

4. Ask students:  Do you think that the particles of a gas are close together or far apart?  How does this compare with your original prediction? Student answers may vary.  Encourage students to realize that gases are composed of particles that are widely separated with a significant amount of space between them.

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5. Ask a student volunteer to draw a particle diagram for a gas on the board.

6. Ask students: Do you think that the particles of a liquid are close together or far apart?  How does this compare with your original prediction? Student answers may vary.  Encourage students to realize that liquids are composed of particles that are not as separated as the particles in gases with less space between them.

7. Ask a student volunteer to draw a particle diagram for a liquid on the board.

8. Ask students:  Do you think that the particles of a solid are close together or far apart?  How does this compare with your original prediction? Student answers may vary.  Encourage students to realize that solids are composed of particles that have no space between them.

9. Ask a student volunteer to draw a particle diagram for a solid on the board.

10. Ask students:  Why do you think the particles of gases are so widely separated? Student answers may vary.  Encourage students to realize that the particles that compose gases have so much space between them because there is very little attraction between the particles.  This allows them to be widely separated and to move independently and rapidly away from one another.

11. Ask students:  Compared to the particles that compose gases, how strong do you think the attraction is between the particles that compose liquids? Student answers may vary.  Encourage students to realize that there is a greater attraction between the particles in liquids, so they are closer together and do not move as rapidly as the particles in gases.  This greater attraction allows liquids to be poured.

12. Ask students:  Compared to the particles that compose liquids, how strong do you think the attraction is between the particles that compose solids? Student answers may vary.  Encourage students to realize that the attraction between the particles is so strong that the particles are fixed in one position preventing them from moving.  The lack of space between particles and their inability to move allows solids to maintain a definite shape.

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G. Conclude this portion of the Investigation by posing the following question:

Ask students: Do you think it is possible to calculate the density of an object that floats and has irregular sides?  How do you think you would do it? Student answers may vary.  

Student answers should indicate that students understand how to calculate the density of a solid.  For example: 

Students may indicate that they could cut the object into a shape that has regular sides and use the formula for measuring volume to calculate the density.  This would work because density is not dependent on the volume of the sample.  

Students may also indicate that they could determine the density of a weight using the volume displacement method and then attach the weight to the object to cause it to sink.  They could then take the difference between the weight and the object and the weight alone to determine the volume of the object.  Density could then be calculated.

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