Tuesday, May 20, 2014

Clash of Clans has Algebra!!!

I like to play the games that my students are playing.  A few weeks ago, they introduced me to Clash of Clans.


At first I thought the game was okay, it must be a teenager thing.  But then I was hooked.  I just need a few more coins so that I could upgrade my elixir storage, and if I upgraded my elixir storage then I could upgrade my gold storage, and if I upgrade my gold storage I could upgrade my elixir collector.  You see what they did there?  Yes, one variable depends on the other.  Right now I'm saving up my gold so that I can upgrade my wizard tower to level 2 (a whopping 360,000 coins) and my elixir so that I can upgrade my barracks to level 7 (240,000 elixir).  

Last night I asked myself if it was worth it.  Should I upgrade my gold mine or let it go?  When you upgrade a goldmine, you are unable to collect any gold during that time.  Here are the details:  My one goldmine is at level 7 and collects 1600 coins per hour.  It costs 28,000 elixir to upgrade to level 8 and takes 24 hours to do this.  Once I'm at level 8 the goldmine will collect 1900 coins per hour.  I thought to myself "Do I really want to upgrade and not have any coins collected in this 24 hour period?  Is it worth it?"  And then it hit me.....this is ALGEBRA!!!

Let x represent the number of hours and let y represent the coins collected.

Equation without upgrading:  y = 1600x + 38400    (the 38400 is the amount collected during the 24 hr period)

Equation without upgrading:  y = 1900x + 0  (0 because you are unable to collect coins from that mine during the upgrade)


At what time with the coins be equal in amount?

Graphically:



Algebraically:

1600x + 38400 = 1900x

38400 = 300x

128 = x
5 1/3 days!!!


I need 360,000 coins to upgrade my wizard tower.  


It would take 128 hours (or 5 1/3 days) for this upgrade to be worth it.  
You can see from this screen shot that I have 201,785 coins right now.


Now my question is, "Will it be faster to collect these 360,000 coins by upgrading this goldmine or by leaving it alone?"

I have a total of 5 goldmines:

Goldmine 1     Level 8     1900 coins per hour
Goldmine 2     Level 8     1900 coins per hour
Goldmine 3     Level 7     1600 coins per hour (thinking about upgrading this one)
Goldmine 4     Level 8     1900 coins per hour
Goldmine 5     Level 3      500 coins per hour
--------------------------------------------------------------
I collect a total of 7800 coins per hour without the upgrade.  I need 360,000 - 201,785 = 158,215 more coins to upgrade my wizard tower.  That would take 158215 / 7800 = 20.3 hours.

Since this would take less than 24 hours to do, it wouldn't make sense to upgrade the gold mine.



I haven't tried any of this with my students yet, but I can't wait to see what individual questions they come up with for their own villages.

Classroom Window Makeover

This is pretty much what my classroom has looked like for the past, oh 6 to 7 years.  I have this beautiful wall of windows and we receive ...