Real World Uses of Exponents

  We usually teach students all the rules for working with exponents after we teach the basic definition.  I don't think I start teaching anything real world until I get to the higher level maths when I teach radioactive decay, population growth and decline, and compound interest.  But what about working it in with the other classes?  How do you do that?  What are some ways exponents are used in real life that we could easily implement in other math classes?

Most of the sites I found that give information on uses in real life only give no more than 4 or 5 examples and even then the examples are just a mention such as exponents are used to determine the spread of disease but its just a mention.

If you go to this site, it has tons of examples of where exponents are used in real life ranging from computers to the size of silicon atoms.  Each example includes details on the way the exponents are used and  includes a visual illustrating the example.  This site even includes an activity for making an exponential decay graph using M & M's.  Most students love doing any type of activity using candy, especially if they know they can eat it when they are done.  At the end, there is a link to a slide presentation you can use in your classroom which contains the same material.  This site is one of the more thorough ones' I've seen.

It has so many examples, the teacher could assign a topic from the presentation to a pair of students who could further research the topic and then the groups could prepare two to three slides in the class presentation.  For instance, the author mentioned the pH scale uses exponents.  I check it out and yes it does indeed.  It actually looks like its more likely a negative exponent because the pH of one means 0.1, a pH of two is 0.01 etc. 

The slide show makes a good starting point for an introduction to the real world uses for exponents.  If you aren't sure how to teach a unit on exponents or what a student should know there is a lovely mind map at this blog.  Although it is focused on junior high, it does have a great layout to see what students should know by the time they hit high school and gives an idea of what to review.

I'm off to do some planning.

Exponents

  Every time I work with exponents in any math class, I notice many of the students still do not have a good understanding of exponents.  I always review exponents in every math class because I end up using them in some way.  So I've been trying to find a visual way to help students understand the concept.

At this point, you are probably wondering why I have a picture of three dogs.  Well, they are a way of expressing exponents in a safe nonnumerical way.  I came across this great page showing how to teach exponents using art.

I might have the above picture to represent dog^2 = dog times dog.  or I might say dog squared = dog time dog.  In this visual representation activity you can use anything as the main object that you are creating exponents with.  It might be ice cream cones, cars, snow machines, anything.

I love it because it shows the base beautifully while letting students utilize the whole concept of exponents.  You could easily create a picture going the other way.  The dog picture would be excellent for dog times dog = dog^2.

Another visual representation is through the use of fractals which is something I'd never even considered. PBS has a great lesson which includes a 3 minute video on using fractals to show positive exponents.  It was great.  It uses the Sierpinski triangle in the video to help show the process.  The activity comes with the whole lesson plan.  Its really nice. 

PBS also had a lesson using the same Sierpinski triangle only for negative exponents.  This one comes with both the lesson plan and the worksheet.  I love the way the short video introduces negative exponents.  The positive exponent video looked at triangles while the negative exponent video looked at lengths of the triangle edges.  I plan to use this the next time I review exponents.

Now I just have to figure out how to teach the laws of exponents with a visualization other than writing it all out.  An example might be (x^2)^3 = (x^2)(x^2)(x^2).  They can see its x^6 but I'm wondering if there is another way of visualizing it.  I'm going to think about it and maybe play around at home.  I hope to put something up on it soon.