Title: Weighing a Dinosaur

Author: Robert Lawrence, D.C. Everest Junior High School, Schofield, WI

Grades: 6-8

Overview of Lesson:
Students focus on methods of science, acting as paleontologists who make inferences about the weight of dinosaurs from models and the density of water.

Suggested Time:
Three class periods. If a written lab report is expected, allow several more days.

Students' Prior Knowledge:
This activity is done after developing the concept that it is possible to approximate the height of an animal from limited evidence. Denver Earth Science Projects module on "Paleontology and Dinosaurs" has an activity called "A Lengthy Relationship" that works well as an introduction to methods of determining size.

There are some difficult concepts in measurement and mathematics involved in this activity. The following questions identify what students know, or think they know, about how a dinosaur can be weighed. Students answer them on a sheet of paper. The sheets are not graded, but are collected and returned as part of the post-lab discussion.

    Questions:
  1. How much did a typical dinosaur weigh?
  2. How did scientists weigh a dinosaur?
  3. Were people around during the Age of Dinosaurs?
  4. Forensic pathologists study the causes of deaths of humans, often using just skeletal remains. How can they estimate the weight of the person based on the skeleton?
  5. If you suddenly became twice as tall and your body kept its current proportions, how many times heavier would you become?
  6. Is the density of your body a lot more than the density of water, close to the same as the density of water, or a lot less than the density of water?
  7. If an object with a volume of 8 cubic centimeters is placed in water, how much water will it displace (that is, push out of the way)?
  8. What does a scale of 1:40 mean?
Background Information:
Paleontologists have found, excavated, and reconstructed skeletons of a variety of dinosaurs. Based on the skeletons, and a comparison of their anatomy to living animals, paleontologists construct models to see what the animals looked like with flesh on the bones. Paleontologists then use the scale models to calculate the mass of the dinosaur.

The models chosen for use in this activity are the Carnegie dinosaur models at the scale of 1:40. These models are considered to be as accurate as our current knowledge will allow. This scale means that 1 cm on this model represents 40 cm on the actual dinosaur. Since volume involves three dimensions (length X width X height), you have to cube the scale factor before using the model's volume to find the volume of the dinosaur it represents. If we assume the dinosaurs were the same density as land animals today, their density would be close to the density of water, which is 1 gram per cubic centimeter. Since we have a reasonable estimate of the density of dinosaurs, and can determine the volume of the scale model dinosaur, we can mathematically determine the mass using the equation for density.

A major concept to be developed through this activity is that physical processes are assumed to be uniform in time and space. As geologists say, "the present is the key to the past". Students need to be aware of the assumptions that are made in this activity.

A second concept is that scientists studying the past use experimentation and scientific method as much as any other scientists. All scientific ideas must be testable.

Student Activity:
1. In this activity, you will be asked to use your measurement skills and mathematical talents to find out how much one species of dinosaur weighed. You will be using a method of experimentation that paleontologists used to calculate the weight of many types of dinosaurs. To stress the methods of thinking scientists use, you will be asked to write the experiment following the PHEOC (Problem, Hypothesis, Experiment, Observations, Conclusion) format.

2. While doing this activity you will be working on state and district standards that require you to:
-Design real or thought investigations to test the usefulness and limitations of a model.
-Explain how the general rules of science apply to the development and use of evidence in science investigations.
-Identify data and locate sources of information including your own records to answer the questions being investigated.
-Use inferences to help decide possible results of your investigations, use observations to check your inferences.
-State what you have learned from your investigations, relating your inferences to scientific knowledge and to data you have collected.
-Evaluate, explain, and defend the validity of questions, hypotheses, and conclusions to your investigations.

3. Lab Format: Use this lab sheet to write notes and information while you do the activity. Your final copy is to be done on loose-leaf paper, in pen or typed.

PROBLEM: How much did a _____________________ weigh?
You will be assigned a species of dinosaur. When you write your report, put in the name of your dinosaur.

HYPOTHESIS: Based on my research, I think that a ____________________ weighed ____________.

A good starting point for your research is The Royal Tyrell Museums fossil encyclopedia at:
http://www.tyrrellmuseum.com/encyclo/index.htm

EXPERIMENT:

    Procedure:
  1. Use the data table to record your information.
  2. Measure and record the length and height of the model.
  3. Multiply the length and the height by the scale factor of 40 to get the size of the dinosaur.
  4. Tie a string around the model
  5. Fill the overflow container with water until the final drop added overflows.
  6. Lower the model into the water. Catch the water that overflows with a graduated cylinder. The volume of the water that overflows is the volume of the dinosaur model.
  7. Remove the model, refill the container, and repeat the measurement to check for accuracy.
  8. Record the volume of the model. The volume of the dinosaur is 40X40X40 times greater. Calculate the volume of the dinosaur (in cubic centimeters).
  9. Convert the volume to cubic meters by dividing by 1,000,000.
  10. Calculate the mass of the dinosaur based on the data you collected from the model.
mass = density X volume

density of dinosaur = density of water = 1000 kg / cubic meter

OBSERVATIONS:
DATA TABLE
TRIAL 1 TRIAL 2
HEIGHT OF MODEL
(cm)
(cm) (cm)
LENGTH OF MODEL
(cm)
(cm) (cm)
HEIGHT OF DINOSAUR
(m)
(m) (m)
LENGTH OF DINOSAUR
(m)
(m) (m)
WATER DISPLACED
(ml)
(ml) (ml)
VOLUME OF MODEL
(cm3)
(cm3) (cm3)
VOLUME OF DINOSAUR =
MODEL VOLUME x40x40x40
(cm3)
(cm3) (cm3)
VOLUME OF DINOSAUR (m3) (m3) (m3)
MASS OF DINOSAUR =
DINOSAUR VOLUME x 1000 Kg / m3
(kg)
(kg) (kg)

CONCLUSION: Based on my measurements, a ____________________ weighed around _____________________.

A conclusion starts by answering the question at the beginning of the lab write-up, then adds interpretation and analysis. For this lab, please respond to the interpretation questions in the conclusion.

1. Convert your own weight (in pounds) to mass in kilograms by dividing your weight by 2.2. (There are 2.2 pounds in one kilogram.)

2. How many times greater was the mass of your dinosaur than your mass?

3. What assumptions have you made in the activity that would influence the accuracy of your results?

4. What effect would the mass of the dinosaur have on the way it moved? Consider Newton's 2nd Law of Motion as you answer.

5. What are possible sources of error in the method used to find the mass of a dinosaur?

6. What is another method that could be used to find the mass of a dinosaur?

    Answers for the interpretation questions:
  1. Convert your weight (in pounds) to mass in kilograms by dividing your weight by 2.2. (There are 2.2 pounds in one kilogram.)
    Answers will vary. A hundred-pound person has a mass of 45 kilograms.
  2. How many times greater was the mass of your dinosaur than your mass?
    Answers will vary.
  3. What assumptions have you made in the activity that would influence the accuracy of your results?
    I assumed that the models are accurate, and that dinosaurs were about the density of water.
  4. What effect would the mass of the dinosaur have on the way it moved? Consider Newton's 2nd Law of Motion as you answer.
    The greater the mass, the greater the force needed to accelerate that mass. The largest dinosaurs probably could not change their speed or direction very quickly.
  5. What are possible sources of error in the method used to find the mass of a dinosaur?
    Possible sources of error would include errors based on the assumptions, errors in the measurement of the water, and errors in the calculations.
  6. What is another method that could be used to find the mass of a dinosaur?
    This is an open-ended question; there are no other methods used.
Teacher Notes: I bought the Carnegie dinosaur models in Sun Prairie, WI at the Dragon's Whistle. They are available at many other better quality toy stores as well. The activity can be done as a station if you want to cut down on the expense of buying many models.

Because of the size of some of the models, the overflow cans have to be large. I used a 5 gallon bucket for the largest models and plastic pop bottles for the smaller models. A hole is cut near the top of the container and a short piece of plastic tubing is inserted to direct the overflow.

The mathematics involved in this activity is very difficult for most middle school students. It takes time to explain the concepts of scale distance and then lead them into scale volume. It also is worth taking the time to lead students through the use of density in this activity.

Extension Activities:
*write a short essay about the limits on the sizes of land creatures.
*An interesting extension to this activity might be to show a short clip from the movie Honey, I Blew Up the Baby. Estimate with the students what they think the scale factor was for the movie, then remind them of the need to cube the scale factor to find scale volume and scale mass. A twenty pound baby at a scale factor of ten would weigh 20,000 pounds! Any human at that size would be reduced to a quivering blob!

Vocabulary: density, scale factor, mass, and weight

Interdisciplinary Connections:
Math: measuring to correct accuracy, multiplication, division, ratios
Language Arts: the use of suffixes and prefixes as they are used in dinosaur names. Wisconsin State Science Standards:
A.8.7
http://www.dpi.state.wi.us/standards/scia8.html
Design real or thought investigations to test the usefulness and limitations of a model.

B.8.3
http://www.dpi.state.wi.us/standards/scib8.html
Explain how the general rules of science apply to the development and use of evidence in science investigations, model-making, and applications.

 C.8.2
http://www.dpi.state.wi.us/standards/scic8.html
Identify data and locate sources of information including their own records to answer the questions being investigated.

C.8.4
http://www.dpi.state.wi.us/standards/scic8.html
Use inferences to help decide possible results of their investigations, use observations to check their inferences.

C.8.6
http://www.dpi.state.wi.us/standards/scic8.html
State what they have learned from investigations, relating their inferences to scientific knowledge and to data they have collected.

C.8.9
http://www.dpi.state.wi.us/standards/scic8.html
Evaluate, explain, and defend the validity of questions, hypotheses, and conclusions to their investigations.

C.8.10
http://www.dpi.state.wi.us/standards/scic8.html
Discuss the importance of their results and implications of their work with peers, teachers, and other adults.

C.8.11
http://www.dpi.state.wi.us/standards/scic8.html
Raise further questions which still need to be answered.

E.8.5
http://www.dpi.state.wi.us/standards/scie8.html
Analyze the geologic and life history of the earth, including change over time, using various forms of scientific evidence.