Let’s grow some grass! November 7, 2010

 

Who knew?  Students love growing grass.  Let me elaborate…. Students love taking care of their grass as they watch it grow- enough to get them to do some pretty complicated algebra.

 

What started out as a simple week-long project that incorporated a bit of environmental sciences (my undergrad background) into algebra became a 10-week long project spanning the curriculum from ecology to linear extrapolation.  It’s been a long time in the making, but beyond a shadow of a doubt this lesson is one of the most engaging that I have created.   My students love the life aspect of the project and hardly complain about doing some pretty complex algebra.   

 

Now, with the magic of a WordPress widget called ”My Shared Files    BOX” (on the sidebar), I was able to upload the Growing Grass Project files onto my blog for all to use! 

 

All three files are important, but the excel workbook includes everything the student needs to create a final portfolio piece, including a formatted final excel sheet that the student can type into and cell directions. 

  

I’m very excited about this and hope that if you do use the project, that you will add a comment to this post on how it went.  I also have other files that go along with the starter ones I posted. 

 

I guarantee that your students will be engaged in their learning and that you will find ways to link most of algebra 1  to what comes up along the way.  

 

WARNING!  This lesson takes on a life of its own!  Proceed with caution! 

 

Now Let’s grow some grass!

 

 

p.s. For supplementary files, you can email me at ZeroSumRuler@gmail.com.  The files include ones on scatter plots and lines of fit as well as a PowerPoint and activity on linear inter- and extrapolation.    

 

Dividing by Zero Blows up the Universe! June 15, 2010

“Because the universe will blow up,” was the usual answer I got when my teachers tried to explain why we couldn’t divide by zero.  From a young age, I was a sort of anti-Pythagorean in that I believed people created numbers, not that the universe was ruled by them.  So why then did we create the divide-by-zero bomb? 

 

The best way I’ve found to describe why dividing by zero will destroy everything is to go back to translating fractions.  What does “1/2” really mean?  “1/2” translates to “1 out of 2” or “I have one piece of candy out of the two pieces on the table, so I have half of what is on the table.  My sister is a good sharer.”

 

Now try this with “0/2”.  This translates to “zero out of 2” or “I have zero pieces of the two that are on the table.  My sister’s cheap!”

 

Both of these situations are real.  You can have one piece of candy out of two.  You can have none of the pieces of candy.  Even if the fraction is an improper fraction, like “3/2”, certainly you can’t have three out of two pieces of candy; this makes no sense at all.  But then we remember that improper fractions can be written into mixed fractions, so “3/2” becomes “1 and ½”, and we sure can have 1 and a half of the pieces of candy on the table [leaving our cheap sister with just ½!  Haha!]!

 

So then comes “2/0”, which would translate to “2 out of zero” or “I have two pieces of candy out of the zero that are on the table.”  HUH??  This obviously doesn’t make sense! Despite what Little Orphan Annie and Jay-Z may lead us to believe, you can’t make something out of nothing.  It’s just basic physics. 

 

Once a student begins learning about slope and functions, the impossibility of “2/0” becomes even more obvious.  Let’s think of a graph that measures your height against your age.  “2/0” represents a rise (y-value or “height”) of 2 and a run (x-value or “time”) of 0.  This is to say that, for example, at time 0 you are 2 feet tall.  Ok, so maybe you were born 2 feet tall.  That’s possible.  Now let’s move up from coordinate (0, 2).  The slope of “2/0” tells us to move up 2 and over 0.  We move up two spaces to 4 feet tall and over to… over to nothing!  We stay at zero!  So a slope of “2/0” says that you can be 2 feet and 4 feet tall at the same point in time.  This is impossible!