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Scale, Proportion, and Quantity

Scientists study natural phenomena that span the full scales of size, time, and energy, from very small to very large. Three major scales distinguish scientific study. The first scale is what can be observed at the macroscopic level, through direct observation with the naked eye. The second scale is what is too small or too fast to observe directly. The third scale is what is too large or too slow to observe directly. In both science and engineering, understanding the concept of scale is crucial to understanding relationships. Quantity, the number or amount of an object or occurrence, is framed by scale. For example, if you are in a ship sailing near Antarctica, the number “ten” would represent a relatively small number of water molecules because there are many more water molecules in the ocean. However, “ten” would represent a relatively high number of other ships in this isolated area. Proportionality and ratios can be used to understand quantity and scale, as well as the relationship between physical characteristics. The depth of the deepest part of the world ocean, the Marianas Trench, can be difficult to conceptualize, but it can be compared to something more familiar to give a sense of scale. At about 11 kilometers (km) deep, almost 100 football fields could be turned on end and stacked inside! Proportion also defines many derived quantities, such as density, speed, and concentration.


Marine and aquatic scientists study phenomena large and small. In terms of size, ocean chemists study compounds in amounts that range from micrograms (0.000001 g) to gigatonnes (1000000 g). On various time scales, ocean scientists study the nerve impulses of sharks, which are very fast, to how ocean life has evolved over billions of years. Scientists use experimental techniques that allow them to observe individual plankton cells (Fig. 1), grow plankton colonies in the laboratory (Fig. 2), and study plankton blooms from satellites in space (Fig 3).

The framework suggests that students can build an understanding of scale through units of measurement. Measurements including weight, time, temperature, and other variables can be assessed and estimated in the classroom. As students progress, they can develop their understanding of proportion and quantities across scales and orders of magnitude. Instruction is needed to help students develop an understanding of ratios and proportion in science. Unlike a fraction of a pie, proportion in science and engineering represents relationships between physical quantities. For example, density is a ratio of mass to volume in an object. Understanding ratios as relationships is important to understanding and interpreting scientific data.


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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.