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Determining the Density of Water - A Graphing Exercise

Grades: 5-8
Author: Jon Valasek
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Abstract

Module Description

Participants will be led through an exercise to devise a strategy to teach students how to properly graph data gained from massing and measuring the volume of different numbers of drops of water and finding the density of water and oil.


Objectives

  • Participants will be able to gather data (mass, volume, and number of drops of water).
  • Participants will be able to graph the data.
  • Participants will be able to produce and implement a lesson plan to lead their students through a discussion of how to graph and solve a problem using the graph.

Materials

Water, cooking oil, electronic balances, 10 mL graduated cylinders, micropipets, and uncooked vermicelli or other pasta. If available, but not necessary - buret and volumetric flask. Graph paper can be printed free online (google search).


Procedures

Overview: Use the following as a guide to read through the procedures in their entirety before attempting to conduct this lesson:

  • Participants are introduced to the micropipet as a means to measure volume.
  • Participants determine experimentally the number of drops of water in whole numbered milliliters of water.
  • Participants graph the data obtained from the previous step.
  • Using the graph, participants find the volume of one drop of water
  • Participants determine experimentally the mass of 5, 10, 15, 20, etc. drops of water.
  • Participants graph the data from the previous step.
  • Using the graph from the previous step, participants determine the mass of one drop of water.
  • Participants graph mass and volume of water.
  • Participants find the mass to volume ratio of water.
  • Participants find the mass to volume ratio of oil.

Engagement

Introduce this investigation by posing the following problem to the participants: Throughout the year you will be using micropipets filled with various liquids to carry out microscale experiments. We will be asked to add 1 milliliter of this or 5 milliliters of that so we need to know how much to add from the micropipette. But these micropipets are not marked. So how can we use these micropipets to measure volumes of liquids? Accept all answers and choose, "by counting the number of drops."

Assessment: Monitor the participation of the participants to make sure that all understand before moving along.

Exploration

Then ask, "So if we know the number of drops, how can we determine the volume measured in milliliters of a number of drops?" This question should incite a number of responses. Divide the participants into small working groups of 3 or 4 and have them brainstorm to answer the question. Have each group report their solutions. A possible procedure would be to use a graduated cylinder and count the number of drops required to fill the cylinder to the 1, 2, 3 etc milliliter marks. Reach consensus as to how to acquire the data. Have each group perform the activity and collect the data.

Assessment: Note how each group is recording the data and have each group report their results. Then ask, "Will the procedure you devised be accurate and work for all volumes?" Have participants discuss their methods. Before accepting comments from each group, perform the following. Take a pipet filled with water and put one drop from the pipet into an empty 10 mL graduated cylinder. Note that the orientation of the pipet determines the amount of water that is dispensed. A good practice is to hold the pipet in a vertical position at all times when dispensing the liquid to ensure uniformity. Emphasize this point to the participants. Pass the graduated cylinder around the room and ask if anyone can tell you the volume of that drop of water. The participants should not be able to accurately determine the volume of that drop of water.

Ask each group of participants to devise a method to accurately determine the volume of any number of drops of water. Give time for brainstorming then have each group report their findings.

Most methods reported will not allow for the accurate determination of the volume of one drop of water. So you might have to lead the groups to consider using graphing methods to solve the problem. Suggest the groups go back to the drawing board and modify their methods to incorporate the use of graphs. Further suggest that they identify the type of graph, components of a graph and methods for finding the line of best fit for the data.

Have groups report their deliberations. This should be a healthy discussion and a number of ideas for teaching graphing should emerge. A possible solution would be to produce a line graph with the following:

  • Title - volume vs number of drops
  • x-axis label number of drops
  • y-axis label volume (mL)
  • x-axis scale 0 to 100 in 1 drop increments
  • y-axis scale 0 to 6 in 0.1 mL increments
  • data points properly entered on graph
  • line of best fit (might not be addressed by every group)

After each group has reported ask, "Using your graphs find the volume of 20 drops of water." Allow each group to report and notice the differences, if any. Exploration of the differences is important to discover the variances in the experiment and what should be controlled. As an example, the drop size varies depending on the angle of the pipet. Another important variable is the volume reading. Parallax can cause improper readings.

Explanation

At this point introduce the concept of significant digits. How many digits should the volume be reported in? The markings on the measuring device determine the accuracy of the device. Normally a 10 mL graduated cylinder has markings to the nearest tenth of a milliliter, so the volume could be read to the nearest hundredth of a milliliter. So the volume of 20 drops of water could be 1.02 mL and should be reported as same. You could use this opportunity to discuss the concept of accuracy as relates to the measuring instrument you are using. This discussion would include the scale of the measuring instrument and interpretation of values between two lines of measurement. Assess the participant's understanding by quizzing them by having them read and record the volume of water (use what you have available) in a beaker, graduated cylinder, volumetric flask, and buret. The most accurate measurement of volume is with a volumetric flask.

Assessment: Ask the participants to determine the number of significant digits they would report in a variety of volume and mass measuring equipment that they use in their classrooms. At this point the participants have gathered volume data and have graphed that data. Next you want to use the graph to find the volume on any number of drops of water. Ask, "What is the volume of 37 drops of water?"

This will be hard for the participants to do since their data is for the number of drops for 1.0 mL, 2.0 mL, etc. Lead a discussion on how to find the answer. To do this have the participants construct a line of best fit through the data points. This is accomplished by taking a piece of spaghetti (vermicelli) and placing it on the graph approximately equidistance between all the data points to include the spaghetti passing through 0,0. This is called the line of best fit. After accomplishing this line of best fit, have the participants carefully trace the line formed by the spaghetti. State, "Now we have a way to determine the volume of any number of drops of water." Take the point on the x-axis representing 37 drops and go directly up from that point to the line you have constructed and make a point on the line of best fit where the 37 drop line intersects. From the point you have made draw a line parallel to the x-axis extending to the y-axis. Then read the volume.

Assessment: Receive input from the group on their answers.

State "Now that we can find the volume of any number of drops of water, find the volume of one drop of water." Accept inputs and note the frustration of finding the answer due to a number of factors: graph and scale size. Rhetorically ask, "Is there a better way to find the volume of one drop of water?"

Answer that there is a more accurate way to find the volume of water using the line of best fit on their graphs. Have the participants recall that the equation for a straight line is y = mx + b where y in our case is the volume, m the slope of the line, which is rise over run, x is the number of drops, and b is the y-intercept, which in our case is 0. So using the equation, the volume of one drop of water would be equal to the slope of the line times the number of drops of water. The slope can be found with the formula (y2 - y1) divided by ( x2 - x1 ), where y2 and y1 are two values of y, and x2 and x1 are two values of x.

Assessment: Have all the participants find the volume of one drop of water and compare results. Also compare these results with the results from the participants' previous examination. They should see that the equation method is more precise.

Exploration

Next have the participants find the mass of any number of drops of water and report the mass of one drop of water. Have them devise the best method and report it to the entire group. One possible method is:

Place a beaker on an electronic balance and add a number of drops until the balance records a mass, then continue to add drops at selected intervals until 100 drops have been massed. Record the results and graph the data. Find the slope of the line of best fit and use the straight-line equation to find the mass of one drop of water.

Assessment: The mass of the number of drops of water should equal the volume of the same number of drops of water.

Explanation

Introduce the concept that all matter has volume and mass and that a substance's mass to volume ratio (mass divided by volume) called density is known. So if we know water's mass to volume ratio we can find its density. Next have the groups brainstorm a way to accurately determine the density of any number of drops of water. Accept reports from the groups by listing possible procedures on the board. The group's discussions should focus on measuring the mass, volume, and number of drops of water; developing a data table to record the measurements. The participants could also devise a way to use the data they have collected to find the density of water. After discussion, the participants should reach a consensus on the procedure to follow. Ideally the groups should decide to use the data they had previously collected. A graph of volume on the y-axis and mass on the x-axis results in the best solution. The slope of the graph should be close to 1 gram per milliliter of water. Water's density is approximately 1.0 gram per 1.0 milliliter.

Elaboration

Finally have the participants find the density of the oil you have provided.

Assessment:

  1. Have the groups report their results.
  2. As a final assessment have the participants write a lesson plan to incorporate this activity into their course.

Rationale

To become scientifically literate students should be able to measure mass and volume, graph data, and solve problems using a graph. These skills developed at an early age are necessary for success in future science and mathematics courses.


Science Standards

NSES Content Standard A: Science as Inquiry: As a result of activities, in grades 5-8, all students should develop

  • abilities necessary to do scientific inquiry
  • understandings about scientific inquiry

NSES Content Standard B: Physical Science: As a result of activities, in grades 5-8, all students should develop an understanding of

  • properties and changes of properties in matter

NSES PROFESSIONAL DEVELOPMENT STANDARD A: Professional development for teachers of science requires learning essential science content through the perspectives and methods of inquiry.

NSES PROFESSIONAL DEVELOPMENT STANDARD B: Professional development for teachers of science requires integrating knowledge of science, learning, pedagogy, and students; it also requires applying that knowledge to science teaching.


Best Teaching Practices

  • Inquiry
  • Systematic approach to problem solving

Time Frame

Participants should be able to complete this exercise in 90 minutes.


Preparation

Obtain enough of each of the materials for each group of three or four participants to use one of each. Place a set of materials for each group to use. Five ounce cups or similar could be used to hold the water and cooking oil.

Notify participants to bring their curriculum guide or textbook to facilitate their production of an implementation plan.


Safety

No special precautions are necessary for handling or disposing of the materials in this lesson.


Assessment

The overall assessment would be to have the participants develop lessons plans and conduct this lesson in their classrooms.


Explanation of Science

Explanations are contained in the procedures.


Handouts

None Available for this Module


Extensions

None


Lesson Implementation Template

Download Lesson Implementation Template: Word Document or PDF File


Equity

Make sure you take into consideration gender and ethnic preferences when assigning participants to groups.


Resources

None available for this module


References

None available for this module