INTRODUCE & APPLY
WEBSITE: The Scale of the Universe
Standard Form, or Scientific Notation, is a means of giving meaning to numbers that are very big or very small; those that are so large or small that they break your brain trying to understand them. They allow us to try and make sense of the absolutely huge, such as the Eridanus Supervoid, down the absolutely minuscule, such as a planck length.
The Scale of the Universe is a fantastic website to give us a sense of scale when considering the universe as a whole. It allows you to zoom in from the largest entities imaginable all the way through, past humans and giant earthworms, to the smallest possible entities.
As well as including scale drawings and labels, the Scale of the Universe also includes the sizes in metres of each entity, in both decimal form and standard form, thus providing the perfect means of introducing the idea of standard form and why it is necessary.
As well as the flash application on the website above, they also provide a video in which someone scrolls through the application for you, which is below if you would prefer. I suggest using the website though as it allows for a more natural conversation with your students as you can change the scale dependent on where the conversation flows.
PRESENTATION: 52!: Dealing with Really Big Numbers
There are 52 cards in a deck, which means there are 52 factorial (52!) ways of arranging them – 52! is a really, really, really big number! It is a number that definitely needs to be represented with standard form as it is almost uselessly large when written in decimal notation.
The above presentation gives one way to try to understand how big 52! is.
The information included in the presentation comes from this WEBSITE, by Scott Czepiel. 52! is of a magnitude that is almost impossible to imagine and the explanation given in the above presentation is a very accessible way of trying to understand it. The website also gives other examples that could be used to accompany this one.
In addition, VSauce produced an excellent video that bring this explanation to life, which you could show as an accompaniment or instead of using the above presentation. The images on the presentation are taken directly from the video. The section of the video that is relevant is from 14:06 – 17:26.