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Practices of Science: Scaling

NGSS Science and Engineering Practices:

NGSS Crosscutting Concepts:

Learning new concepts can be very difficult. Diagrams and animated images can be useful in explaining abstract concepts, such as the causes of lunar and solar eclipses, the Earth’s seasons and the phases of the moon. Diagrams help people, even seasoned scientists, to imagine the relative positions of the earth, the sun, and the moon, all in moving three-dimensional (3-D) space over time. However, these diagrams can also be misleading. Many of the captions of figures of the sun, moon, and earth in Exploring Our Fluid Earth warn that the depicted objects are not drawn to scale. Instead, the actual sizes of the earth, the sun and the moon—and the vast distances between them in outer space—have been distorted to allow for easier viewing.

 

True or uniform scaling is the enlarging or shrinking of objects in a manner that preserves the object’s original proportions. For example, some toy cars and trains are scaled-down models of the original objects. The most common model trains are 1/87th the size of real trains, so that a typical 12 meter long boxcar is transformed into a toy only 14 cm long. Not only is the boxcar’s length scaled down, but all other dimensions and features are also similarly shrunken to preserve the train’s original proportions.

 

True-to-scale models can be very useful in science. For example, they can be used to enlarge objects that are very small. A biology classroom might have a scaled-up model of a single plant cell. Tiny green chloroplasts might be difficult to see under a microscope, but they would be easy to visualize in the true-to-scale model.

 

<p><strong>SF Fig. 6.12.</strong> (<strong>A</strong>) An exaggerated diagram showing the elliptical orbit of the moon around the earth.</p><br />
<p><strong>SF Fig. 6.12.</strong>&nbsp;(<strong>B</strong>) An accurate diagram showing the movement of the moon around the earth. Note that in both these diagrams the distance between the earth and moon is not to scale.</p><br />


A true-to-scale proportional transformation can make the implied relationships between objects confusing. For example, SF Fig. 6.12 A depicts the elliptical orbit of the moon around the earth with an exaggerated oval-shaped orbit. A true-to-scale depiction of this relationship is shown in SF Fig. 6.12 B. Both images have distorted object sizes and distances. Although this true scale figure is accurate, it may be difficult to envision the moon’s elliptical orbit from this figure. This is because in a true-to-scale diagram of the moon’s orbit the distance between the Earth and the moon varies very little, by only about 10% (SF Fig. 6.13).

<p><strong>SF Fig. 6.13.</strong> Earth and its moon, depicted true-to-scale. White bar underneath the moon indicates maximum and minimum distance from Earth at apogee and perigee, respectively.</p><br />


 

Question Set: 
  1. Think of three difficult or abstract science concepts that you think would benefit from true-to-scale models. Think of three science concepts that you think would be made more confusing, or would not convey the information accurately, in a true-to-scale model.
     
  2. A typical classroom globe (about 41 cm diameter) is a scaled model of Earth.
    1. At this scale, how big would a model of the sun need to be?
    2. How big would the moon need to be?
    3. How far away would the sun, moon, and earth need to be for your model to be accurately true-to-scale?
       
  3. Try to make your own true-to-scale model of our solar system. Begin by considering the smallest and most distance objects in your model first before moving onto the larger and closer objects.

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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.