Scale, Proportion, and Quantity

"The difference between living and half living is seeing well, looking for associations between things, seeking the connections, being aware of scale and proportion.

Alexandra Stoddard

Quantity refers to the amount of something. Scale and Proportion are about how the size or quantity of something relates to the size or quantity of something else. In math class, we learn about ratios to describe the relationship between these quantities. We also learn about dilation in math to show how the size of an object can change, but the proportion of one length to another stays the same.

In science, we use Scale and Proportion to find meaning in the measurements we make. One number by itself will not show us any patterns. We need to compare numbers to see if and how they are related to each other, which will lead us to determine if there is a connection of any kind. However, it can be quite difficult to compare sizes or amounts when the objects or distances you are measuring are very large or very small. How can you compare the orbit of an electron around the nucleus to the orbit of the earth around the sun? The same can be true if you are talking about measurements of time. It is difficult to compare something happening in less than a nanosecond to something that takes millions of years to occur. Scale and Proportion give us a lens to help make those differences less difficult to navigate, and allow us to compare things that would otherwise be impossible.

For example, the radius of an electron’s orbit around the nucleus in an atom is about 50,000 times larger than the radius of the electron itself. The radius of the earth’s orbit around the sun is about 23,500 times larger than the radius of the earth. So to compare them at scale, we would say the ratio of the orbit to the size of the object orbiting is more than 2 times greater for the electron than for the earth. Scale and Proportion allow us to compare things that were not otherwise comparable. This allows us to use math to explain our observations, giving quantitative evidence that support the claim we are making. This makes the argument much more convincing and harder to refute.

Writing and Speaking about Scale, Proportion and Quantity

Students often struggle with how to discuss Scale, Proportion, and Quantity when writing, or when speaking with their peers. Here are some sentence frames to help you with the discussion:

How does the proportion of ___________ to __________ affect the ________________?
How does the relationship between ____________ and _________ change when examined over longer periods of time.
How can the ideal ratio of ____________ to ___________ be found, when determining _______________?
How does one know what measurement scale to use when comparing __________ and ___________?
When ____________ and ____________ are compared at a smaller scale, it is easier to see _______________.
The ratio of _____________ to _____________ shows that ________________ increases/decreases/stays the same over time.
It is impossible to determine _______________ at this scale. It needs to be explored at a much bigger/smaller scale.
A pattern is seen when comparing these values. ___________ is always ________ times bigger/smaller than ______________.
There is no conclusive pattern seen. The proportions between __________ , __________ , and ___________ are inconsistent as _______________ changes.