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CCC3: Scale, Proportion, and Quantity

In considering phenomena, it is critical to recognize what is relevant at different measures of size, time, and energy to recognize how changes in scale, proportion, or quantity affect a system's structure or performance. (NRC Framework 2012, p. 84)

Introduction to CCC3: Scale, Proportion, and Quantity

from NGSS Appendix G - Crosscutting Concepts





K-12 Progressions

from NGSS Appendix G - Crosscutting Concepts

K-2 3-5 6-8 9-12
Scale, Proportion, and Quantity

Students use relative scales (e.g., bigger and smaller; hotter and colder; faster and slower) to describe objects. They use standard units to measure length.

Students recognize natural objects and observable phenomena exist from the very small to the immensely large. They use standard units to measure and describe physical quantities such as weight, time, temperature, and volume.


Students understand the significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs. They recognize patterns observable at one scale may not be observable or exist at other scales, and some systems can only be studied indirectly as they are too small, too large, too fast, or too slow to observe directly. Students use orders of magnitude to understand how a model at one scale relates to a model at another scale. They use algebraic thinking to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth).

Progression of CCC3: Scale, Proportion, and Quantity

from A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (pages 90-91)

The concept of scale builds from the early grades as an essential element of understanding phenomena. Young children can begin understanding scale with objects, space, and time related to their world and with explicit scale models and maps. They may discuss relative scales — the biggest and smallest, hottest and coolest, fastest and slowest — without reference to particular units of measurement. Typically, units of measurement are first introduced in the context of length, in which students can recognize the need for a common unit of measure — even develop their own before being introduced to standard units — through appropriately constructed experiences. Engineering design activities involving scale diagrams and models can support students in developing facility with this important concept. 

Once students become familiar with measurements of length, they can expand their understanding of scale and of the need for units that express quantities of weight, time, temperature, and other variables. They can also develop an understanding of estimation across scales and contexts, which is important for making sense of data. As students become more sophisticated, the use of estimation can help them not only to develop a sense of the size and time scales relevant to various objects, systems, and processes but also to consider whether a numerical result sounds reasonable. Students acquire the ability as well to move back and forth between models at various scales, depending on the question being considered. They should develop a sense of the powers-of-10 scales and what phenomena correspond to what scale, from the size of the nucleus of an atom to the size of the galaxy and beyond. 

Well-designed instruction is needed if students are to assign meaning to the types of ratios and proportional relationships they encounter in science. Thus the ability to recognize mathematical relationships between quantities should begin developing in the early grades with students’ representations of counting (e.g., leaves on a branch), comparisons of amounts (e.g., of flowers on different plants), measurements (e.g., the height of a plant), and the ordering of quantities such as 
number, length, and weight. Students can then explore more sophisticated mathematical representations, such as the use of graphs to represent data collected. The interpretation of these graphs may be, for example, that a plant gets bigger as time passes or that the hours of daylight decrease and increase across the months. 

As students deepen their understanding of algebraic thinking, they should be able to apply it to examine their scientific data to predict the effect of a change in one variable on another, for example, or to appreciate the difference between linear growth and exponential growth. As their thinking advances, so too should their ability to recognize and apply more complex mathematical and statistical relationships in science. A sense of numerical quantity is an important part of the general “numeracy” (mathematics literacy) that is needed to interpret such relationships. 

Performance Expectations Associated with CCC3: Scale, Proportion, and Quantity

K-2 3-5 6-8 9-12
N/A 3-LS4-1


Additional Resources

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (pages 89-91)

NGSS Appendix G - Crosscutting Concepts

Bozemanscience Video
