Sometimes UN-Simplified is Better

To Simplify or Not to Simplify, that is a good question.

Recently, I have not been simplifying my work.  Let me explain.  We have been working on finding the equations of sine graphs in Precalculus.  I have found that when I type out my work in Desmos it doesn't automatically simplify it.  It still graphs it.  You can see the changes as you type them in.
This is really cool.  It leaves it so that the students can think about how the numbers came to be.  It is almost formula like.   See below.
 

Then, I asked my students to simplify the equation so that we can gain meaning out of the numbers.

Here is the project we just finished with if you are interested in taking a look. It is a project where we look at the vertical height of a person on a swing.  There is data involved and then we have to find the correct sine wave.   http://tinyurl.com/swingdesmos


Here is another place that I see non-simplification as a perfect fit.  In linear equations using slope. You can see here it fits right into the slope formula.  This also shows equivalencies of linear equations.   So if you make a mistake on one simplification step, you will see it right away because it will not match up with the first one.

Actually, I think that when we show our steps in this way we are "digitally showing our work."  Hope you can give it a try.

Best,
Dave