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Activity: Measuring Whale Dimensions
NGSS Science and Engineering Practices
Using Mathematics and Computational Thinking
Constructing Explanations and Designing Solutions
NGSS Crosscutting Concepts
Scale, Proportion, and Quantity
NGSS Disciplinary Core Ideas
LS1.A: Structure and Function
ETS1.C: Optimizing the Design Solution
Table of Contents
Activity: Measuring Whale Dimensions

Materials for Part A

  • Fig. 6.16
  • Ruler
  • Printer and paper
  • Pen or pencil

Materials for Parts B and C

  • Fig. 6.17
  • Fig. 6.17.1
  • Fig. 6.18 C
  • Two laser pointers (Safety note: never point a laser at someone’s eye and never look directly into a laser beam)
  • Ruler
  • Meter stick
  • Tape measure or transect tape
  • Tape
  • Projector
  • Calculator
  • Sticky notes
  • Digital camera

Procedure

A. Estimate the length of a whale using markers in a photo

 

<p><strong>Fig. 6.16.</strong> (<strong>A</strong>) Sperm whale (<em>Physeter macrocephalus</em>) mother and calf underwater side view with red dot marks 50 centimeters apart</p>

Fig. 6.16. (A) Sperm whale (Physeter macrocephalus) mother and calf underwater side view with red dot marks 50 centimeters apart

Image by David Lin, adapted from Gabriel Barathieu, Flickr

<p><strong>Fig. 6.16.</strong>&nbsp;(<b>C</b>) Sei whale (<em>Balaenoptera borealis</em>) mother and calf as seen from an aerial survey</p>

Fig. 6.16. (B) Sei whale (Balaenoptera borealis) mother and calf as seen from an aerial survey

Image by David Lin, adapted from Christin Khan, National Oceanic and Atmospheric Administration (NOAA)

  1. Choose one of the photos in Fig. 6.16. Both photos show a whale marked with two red laser points 50 centimeters (cm) apart.
     
  2. Print the photo so that it takes up a whole page.
     
  3. Use your best judgment to predict the length of the whale in meters.
     
  4. Estimate the length of the whale using the following formula, where E is the estimated length and K1 is the ratio of the length separating the red laser pointers in real life to the length separating them on your printed photo.

 

 

Example:

If the laser points are set at 50 cm apart in real life and the length of the laser points on the printed photo is 1 cm, then K1 = 50 cm/1 cm = 50.

If the whale measures 19 cm on the printed paper, then E = 50 × 19 cm = 950 cm = 9.5 meters (m)

B. Engineer a laser-measuring device

  1. Carefully consider the diagram of a laser pointer measuring device in Fig. 6.17, and gather the materials you will need to build your own.

 

<p><strong>Fig. 6.17.</strong> Diagram of laser pointer measuring device, with 50 centimeters between the laser beams.</p>

Fig. 6.17. Diagram of laser pointer measuring device, with 50 centimeters between the laser beams.

Image by David Lin

  1. Using tape, attach one laser pointer so that the center of the laser beam is at the 25 centimeter (cm) mark on the meter stick. Make sure that your laser pointer is perpendicular to the meter stick.
     
  2. Using tape, attach the second laser pointer so that the center of the laser beam is at the 75 cm mark on the meter stick. Make sure the laser is pointing in the same direction as the laser pointer in step 1.The two laser pointers should be parallel to each other.
     
  3. Shine the laser pointers directly on the floor or on the wall (no more than 10 cm away from where you are standing).
    1. Measure the length of separation between the lasers. It should be very close to 50 cm.
    2. Adjust your lasers as needed to make sure they are parallel.
       
  4. Calibrate your device. Stand about three to eight meters (three to four body lengths) away from a chalkboard or wall. Point the laser-measuring device at the wall. Be sure that the lasers are pointing directly at the chalkboard or wall, and not at an angle.
     
  5. Have another group member mark the location of the laser dots using chalk or post-it notes.
     
  6. Measure the length between the two marks. The length should be the same as that between the lasers pointers on the meter stick (about 50 cm). If the length between marks is different, your lasers are probably at an angle.
     
  7. Adjust the device as needed and repeat steps 4–7 until the wall measurement matches your device measurement.

C. Use your laser pointer device to estimate the length of a large object in your classroom

  1. Find an object in your classroom that is at least one meter in length.
     
  2. Estimate the length of the object using the laser-measuring device.
    1. Stand three to eight meters away from the object. Use the laser-measuring device to shine the lasers on the object.
    2. Take a digital photo so that the laser points are visible. If needed, highlight the location of the two laser points using sticky notes.
    3. Print the photo.
    4. Measure the distance between the two laser points in the printed photo in centimeters.
    5. Calculate the constant K1 for your scaling equation.
    6. Measure the length of the object on the printed photo in centimeters using a ruler to find the true length (T).
    7. Calculate the estimated length of the object E using the constant K1 and the measured length on the printed photo.

 

 

Example:

If the lasers are 50 cm apart in real life, and the laser marks are 5 cm apart on the printed paper, then K1 = 50 cm/5 cm = 10

If your printed whale is 20 cm long, then E = 10 × 20 cm = 200 cm = 2 m.

  1. Measure the length of the object using a tape measure to obtain its true length T.
     
  2. Calculate the error of your estimated distance. For this activity, 25 percent or less is considered to be an acceptable. If your error is larger than 25 percent, you may need to repeat this process starting over from part B (calibrating your device).

 

Example:

The estimated length E is 200 cm as calculated above. If the true length T is 180 cm, then our percent error = [(200 – 180)/180] x 100 = 11 percent error

D. Measure the length of a marine mammal (optional)

  1. Choose one of the photos in Fig. 6.17.1.

 

<p><strong>Fig. 6.17.1.</strong> (<strong>A</strong>) Sperm whale (<em>Physeter macrocephalus</em>) as seen from an aerial survey</p>

Fig. 6.17.1. (A) Sperm whale (Physeter macrocephalus) as seen from an aerial survey

Image courtesy of Tim Cole, National Oceanic and Atmospheric Administration (NOAA)

<p><strong>Fig. 6.17.1.</strong>&nbsp;(<strong>B</strong>) Atlantic spotted dolphins (<em>Stenella frontalis</em>)</p>

Fig. 6.17.1. (B) Atlantic spotted dolphins (Stenella frontalis)

Image courtesy of Bmatulis, Wikimedia Commons

  1. Using a projector, project the marine mammal photo on a screen or wall.
     
  2. Using you best judgement, predict the length of the marine mammal in meters.
     
  3. Calculate the constant K1.

 

  1. Get the K2 value from your instructor. Since you will not be able to project the true size of the organism, a second scaling constant K2 is needed. K2 is the ratio of the length of the whale in real life to the length of the projected whale.

 

  1. Estimate the length of the whale (E) using both K1 and K2

 

E. Humpback whale body length calculation using fluke width

  1. Observe the humpback whale from Fig. 6.18 C projected by your instructor. Note that the whale fluke is close to, but not exactly, actual size.

 

<p><strong>Fig. 6.18.&nbsp;</strong>(<b>C</b>) Humpback whale fluke</p>

Fig. 6.18. (C) Humpback whale fluke

Image courtesy of Amy Kennedy, National Oceanic and Atmospheric Administration (NOAA)

  1. Based on the size of the fluke, predict the length of the humpback whale.
     
  2. Use the scaling method outlined in part B step 3 to estimate the width of the whale fluke.

 

  1. Calculate the estimated body length of the humpback whale using the following equation.
    body length in meters = 0.77 + 2.9 × fluke width in meters
    Note: This equation was adapted from Sousa-Lima, R.S. and K.R. Groch. 2010. Correlation between body length and fluke width in humpback whales, Megaptera novaeangliae. Marine Mammal Science 24(4):977-981.

 

Activity Questions
  1. What is scaling and how did the K constants help to scale the image measurements to real life measurements?
     
  2. Compare your measurement results with those of your classmates. Were your results similar? Explain any differences.
     
  3. A marine mammal biologist is trying to measure a whale from a small inflatable boat. What are some of the logistical challenges that he or she faces in measuring a whale’s size? Explain.
     
  4. What are some limitations to measuring distances using this a scaling technique method? What are some limitations to measuring areas?
     
  5. Using Fig. 6.17.2, estimate
    1. the average humpback whale length.
    2. the maximum and minimum possible whale lengths.
       
  6. How does the estimated length of the humpback whale you calculated compare with the average humpback whale length? The minimum? The maximum?
Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.