Density

Developers:

Sharon J. Kelly, M.Ed.
Upper Dublin Schools
Ft. Washington, PA

Andrew L. Meyer, Ph. D., Senior Scientist
Rohm and Haas Company
Spring House, PA

Grade
Levels:

Primary:
This unit is a series of four experiments that allows primary students to use the study of density to learn the scientific process. The children will have an opportunity to manipulate the materials and measures themselves, record data, and draw conclusions while working in whole group situations with teacher direction and/or in small cooperative groups. They will record their data on a rank order line where they will work on the math concepts of greater than, less than, and equal to. They will write up their conclusions using correct scientific language and format. They will draw a concluding picture of how the density of materials affects their lives. Questions and ideas need to be encouraged and seen as both an opportunity to teach and as a springboard for further investigation. "Let's find out" is the optimal phrase.

Fourth and Fifth Grades:
This unit could be used as an opportunity to reinforce the math skill of division. By using a scale or a primary balance with weights and by measuring volume, the students can obtain the numerical values needed to calculate the bulk density of materials. In another of the experiments, the students obtain the data needed to determine the absolute density. For example, if 30 ml of corn syrup weighed 36 g, the absolute density of corn syrup is calculated by 36 g / 30 ml = 1.20 g/ml.

Older students could also write up the experiments and their conclusions whereas the younger students would be dependent on oral discussion to express their ideas.

Disciplines:

General Science, Language Arts, Math

Student Goals:

On completion of this unit, the student will have:

1. Understood that science is a tool we use to make sense of what we observe and to gain new knowledge.
   
2. Learned the elements of the scientific method, i.e., careful measurements and observation, changing one variable at a time, generating and testing hypotheses, and repeatability.
   
3. Learned to record results.
   
4. Learned to draw inferences and connect his knowledge to his world.
   
5. Understood that the scientific process is something he can do.

Student
Objectives:

On completion of this unit, the student will be able to:

1. Explain orally the relationship between density, weight, and volume.
2. Explain by way of example the difference between bulk and relative density.
   
3. Explain orally how the relative density of a material determines whether it sinks or floats.
   
4. Make hypotheses about the density of materials.
   
5. Work independently or in a small group to experimentally obtain data on the density of self selected materials.

Background:

Density is defined as the ratio of the mass of a material to its volume. It may be understood in three senses:

1. Absolute Density: the density of a material in its closest packed form.
   
2. Relative Density: the density of a material relative to another material, commonly water.
   
3. Bulk density: the average density of a material which consists of individual macroscopic particles, i.e. not atoms or molecules. Bulk density may change with the degree of compaction, e.g. freshly fallen snow vs. a packed snow ball.

For most purposes the absolute density of a liquid is equal to the relative density of that liquid compared to water.

For a given volume, the weight of a material is directly proportional to its density. Thus, a more dense material is heavier for a given volume. In other words, a more dense material weighs more for a given volume than does a less dense material.

For a constant weight, the volume of a material is inversely proportional to its density. Thus a more dense material occupies less volume than does the same weight of a less dense material.

Introduction of
These Concepts
to the Students:

1. Teach the concept of volume: the space that something occupies.
   Use a balloon to demonstrate that the volume of an empty balloon is less than the volume when it is blown up.
   
2. Show the students that they are already aware of bulk density.
   For example:
   Act out the snowflake example.
   Get 10 sheets of paper, crumple 5. Compare the volumes of the crumpled paper to the flat paper.
   Weigh a given volume of Rice Crispies and then measure the weight and volume after crushing them.
   Weigh and compare the volume of popcorn before and after popping. (Then eat it.)
   These examples should lead the children to conclude that the same material has a greater density when its parts are close together than when they are far apart.
   
3. The concept of relative density will be introduced when the students observe that materials like rice, which were observed to have a bulk density less than water, actually sink in water. They should either conclude on their own or will be told that the low bulk density occurs because there is air between the particles. (Bulk density is actually the average density; it is the sum of the weight of the particles and of the air between them divided by the volume.)

Experimental
Notes:

It is critical that the volume of the materials used for experiments 1,2, and 4 be the same for each determination. Any measuring device may be used so long as the volume can be controlled to be the same for all experiments. We are recommending baby food jars because they are readily available and in our experience are relatively uniform in volume; our jars averaged 124+/- 1 ml. In each case care must be taken to fill the jars completely to the top. (Of course, materials whose particles are large like stones or marbles will not allow complete filling of the jars.

When working with primary students, their inability to accurately measure materials and read a calibrated cylinder will result in data that would be found incorrect if more sophisticated methods were used by more sophisticated students. They will not be able to measure the small difference in water and cooking oil. The concept of the density of one material being similar to another material is acceptable for our purposes in the primary grades.

If using a double pan balance, we recommend pennies as the weights because they are uniform in weight. Moreover, the weight of each penny is relatively small allowing small increments to be measured.

Experiment 1: Ranking Substances by Density

Goals:

1. The students will learn the experimental technique.
   
2. The students will become active scientists.
   
3. The students will understand that the study of science requires precision and repeatability.
   

Objectives:

1. The students will learn the experimental techniques necessary for Experiment
   
2. a. The students will use a primary balance or a scale correctly.
   b. The students will transfer the materials completely.
3. The students will record data by using the rank order line for primary grades or by tabulating the calculated densities when the students are capable of division.
   
4. The students will be actively involved in the experiment.
   
5. The students will cooperate with others to complete the scientific tasks.
   

Materials:

baby food jars
primary balance
pennies used as weights
jars filled with water, sand, corn syrup, Rice Crispies, ground coffee
colored paper in the shape of baby food jars
white paper in the shape of baby food jars
rank order line made by the teacher

Procedure:

1. Estimate the order of density of the substances:
   A. With all the jars marked as to their contents, pass the jars around to the children and ask them to make a judgement about Encourage the children to use the terms greater than, less than, shapes and placing them on the rank order line.
   
2. Test the student's judgments by weighing the contents of the jars:
   With teacher supervision:
   A. Have the students weigh the jars using either a primary or a scale.
   B. Have the students record the weight or the number of pennies on a white jar shape and place it on a rank order line. White jar shapes are used to distinguish data determined by measurement from data determined by estimation or hypothesis which was recorded using the colored jar shapes.
   C. Ask the students if they have drawn any conclusions or want to make a hypothesis about their observations. Keep in mind that some conclusions are also hypotheses which may need to be tested. (A hypothesis is an unproved statement which accounts for the observations or conclusions.)
   D. Record conclusions and/or hypotheses for future reference.
   
3. Group ranking of additional materials:
   A. Divide the class into groups.
   B. Give each group a jar containing one of the initial test materials. Also give each group jars containing 3 additional materials. Each group should get the same 3 additional materials.
   C. Have the students repeat Step 2 in their groups.
   D. Bring the class together and report and record their results on the rank order line. All groups should get approximately the same results if the differences in densities between materials are not too small to measure. The teacher could ask the students to make hypotheses as to why their results differed. For older students it would be good to emphasize that repeatability is the hallmark of good science and they should be able to duplicate their results.
   F. Ask the class to suggest ways to solve the problem of how to rank materials whose density is similar. Good ways might be to measure them using weights with a smaller increments between them such as plastic poker chips or matches, or to use larger amounts of the materials so that the incremental difference in weights would be a smaller fraction of the total weight. Discuss the merits of other ideas and test them if time allows. Younger students may be satisfied to know that the density of some material is equal to the density of another.
   

Experiment 2: Further Ranking Substances by Density

Objectives:

1. To further involve the students in recognizing the concept of density in their everyday experience.
   

Materials:

Have the students bring in materials of their choosing from home in filled jars.Other materials to be included are rice, cooking oil, wood (These materials and their density will be needed for Experiment 3 also.)

Procedure:

1. 1. Have the students estimate the rank order of their materials.
   A. Circulate some of the jars containing materials from Experiment 1 and the jars containing materials the students brought in.
   B. Have the children write a sentence or two predicting where their materials would be positioned on the rank order line and why. Remind them to think of their conclusions or hypotheses from Experiment 1. This could be done individually or in small groups.
   
2. Rank the materials by density.
   A. Repeat steps 2 A, B, and C from Experiment 1.
   B. Ask the children to discuss why their prediction was close or not to the observed ranking.
   

Outcomes from Experiments 1 and 2

In these two experiments the students have made subjective judgments about the rank order of several materials by density and have tested whether these judgments were born out by experimentation.

They have learned the usefulness of recording their results.

They have been asked to draw conclusions and make hypotheses based on the observations from Experiment 1 which were or could be tested in Experiment 2.

Experiment 3: The Inverse Relationship of Volume and Density

Goals:

1. The student will observe that if the weight of several materials is held constant, the volume will be found to be greater for less dense substances.
2. The students will discover the concept of relative density.
   

Objectives:

1. The students will be able to provide reasons orally or in writing for the rank order established by testing.
   

Background:

In this experiment the students will be learning another way of evaluating or ranking materials by density. By placing solid materials in water only the volume taken up by the particles is measured. The effect of the air between the particles is eliminated. This will allow the students to recognize the differences that will lead to the concept of relative density. Once this concept is understood, it will allow them to better understand their world by understanding the principle which explains why things float or sink in water.

Materials:

primary balance or scale
100 ml. plastic graduated cylinders
selected materials from Experiment 1 and 2 or other appropriate materials.
These should include solids that float such as wood or butter and at least one liquid that floats such as cooking oil. Rice should also be included. (See below.)
pennies for weights

Procedure:

1. Select an arbitrary weight to be used for the experiment. This should be large enough so that materials with large, heavy particles can be used and small enough so that amount of the smaller, less dense particles is not too great to put into a cylinder.
   
2. Have the students predict whether the materials used will float or sink using the chart in the appendix to record their prediction. The chart will be completed as the experiment continues.
   
3. Put about 40 ml of water in the plastic graduated cylinder. You may want to mark that level with tape so the students can clearly see the beginning water level. Younger students may have difficulty reading small increment marks.
   
4. If a primary balance is used, balance an empty jar with pennies or other suitable weights. In the case of a scale weigh the empty jar; the teacher will then have to make the children understand that the weight of the material is the difference between the weight of the jar with its contents and the weight of the empty jar.
   
5. Add the amount of each material to the jar until it balances or until it has the required weight.
   
6. Place the contents of the jar into the cylinder and measure the increase in the volume of the water. If the material floats, it will be necessary to use a rod or some other device to push it just under the surface of the water, taking care not to displace additional water with the rod.
   For liquids, be they less dense or more dense than water, the water displacement is superfluous because their volume could be measured directly in the cylinder. However it is recommended to use the same experimental method for all the determinations so as not to confuse the students.
   Older students might not be confused by using different procedures to get the volume. For them it could be instructive to measure the volume of the liquids by both methods to show that the results are the same. Likewise, they should get the same numerical value for the density of the liquids that they determined in Experiments 1 and 2.
   
7. Record the number of ml of water displaced on a white cut out jar and place it on the ran order line.
   
8. Repeat the procedure with the remaining materials completing the chart after each material.
   
9. With all the students able to see the rank order line from Experiment 1 and 2 and the rank order line from Experiment 3, discuss the similarities and differences and why they may have occurred.

Notes:
This experiment can be thought of as testing the hypothesis: If popped popcorn is less dense than the same weight of unpopped corn, then its volume should be greater.

Plastic graduated cylinders are recommended so the students can handle them safely. They are inexpensive and available from scientific supply houses. Other measuring devices could be substituted so long as they have narrowly spaced gradations.

In this experiment students should conclude that materials less dense than water will float on it. But they also will observe that rice which had a bulk density less than water sinks. This observation is an indication that the students' current understanding of density is incomplete and that their "theory" must be modified to incorporate the fact that some materials which seem to be less dense than water sink. In this way they can come to an understanding of the concept of relative density. Perhaps they will independently come up with the idea that the air between the particles makes the bulk material appear less dense than the particles that make it up.

Experiment 4: Using Flotation as a Way of Evaluating the Density of Materials

Background:

The greater the weight of the cargo, the lower a boat floats in water. Thus the depth to which a floating container sinks in water is a measure of the weight in the container. This idea can be used in place of, or in addition to, a balance and weights to rank the weight of a given volume of a material.

Objective:

1. The children will discover another way of determining the rank order of materials by density.
   

Materials:

a 1 or 2 liter transparent soda bottle with the neck cut off
many smaller diameter plastic bottles whose length are much greater than their width or diameter and which fits inside the soda bottle with out too much friction. A scale in centimeters or quarter inches should be marked on the side of these bottles. (See drawing below.)
test materials from Experiment 1 and 2
baby food jars from Experiment 1 and 2
pennies or other suitable ballast to keep the inner bottle floating upright if necessary
rank order line
jar shapes for recording data

Procedure:

Review with the students what they learned about density when they used the balance. Discuss that now they are going to use another method of determining the rank order of materials. As an introduction the children could be asked to discuss how the weight of the material in a boat effects how it floats.

With the students doing the work, but the teacher directing the experiment:

1. Fill the soda bottle half full of water.
   
2. Have the children predict the order of the materials based on their previous experiments and record their predictions using colored cut outs as before.
3. Place the contents of the baby food jar into the inner container.
4. Float the inner container in the soda bottle. Observe how low it floats based on the markings on the side of the inner container.
5. Have the children record the observation on white cut outs and place them on the rank order line.
6. Alternatively, after a few demonstrations, the children can be divided into groups. They would be instructed to make the measurements on several materials themselves and then report back to the whole group later.
   

Conclusion:

Bring the children together with the three rank order lines and ask them what conclusions they can draw from the experiments about the weight of the materials and their densities. They should be asked to compare the rank order of the materials as determined in Experiment 1 and 2 and in Experiment 4. They should see that the rank order is the same and conclude that this method also confirms the results of Experiment 2.

What did they learn from Experiment 3? Help them see the inverse order of the materials on the rank order line. The densest material, the one that required the least volume to balance the assigned weight, took up the least amount of space when put into the water.

The children should be asked to think about how this knowledge of density could be useful in their lives. Examples might be deciding how full they can fill their cereal bowls with cereal that is more or less dense than milk. Or how to pack their suitcase to get the most clothes in it. Younger children might enjoy drawing a picture depicting how the density of a material affects their lives.

Extensions:

1. Test different kinds of cereals to see which are more dense or less dense by adding them to milk. Have the children bring in many different kinds of cereals.
   
2. Giving each student or each group of students a ball of clay or a piece of aluminum foil, have them form a boat that will float when an equal amount of a designated material is put in it. Have a big tub of water and allow the students to learn by trial and error. When they have built a boat that floats with the material in it, have them draw a picture of it. Tell them to take care to get the length and width measured exactly. When all the pictures have been drawn, discuss as a group what kind of boat was needed to float the material. Have the children predict what kind of boat would be needed to carry a heavier material or a lighter material. They could make those boats as time allowed.