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Saturday, August 16, 2014

Probability Activity - Adapted from Stone Librande

In my last post I wrote about a Probability Activity created by Stone Librande.  In this post I will adapt what he has created, but the credit goes to him.

Activity #1:  Create the Best Die


Give each student a blank die (or stickers on a regular die that they could write on).  Each student can write any number they want on each of the sides, but they still need to have a sum of 21.  Also, the students cannot use the number combination 1, 2, 3, 4, 5, 6.    Game play is that two students each roll their die, the player with the bigger number gets a point.  This is repeated until one of the students has 10 points.  The students keep switching partners to see how many times they can win.

After the students have used experimentation to determine the best die, take a look at why.
Suppose Player one used the numbers 3, 3, 3, 4, 4, 4 on his die, and player 2 used the numbers 0, 2, 2, 4, 5, and 8 on his.  Below is a chart of the different outcomes.  Gray is a tie, blue is a win for player 1, and red is a win for player 2.  You can see out of 36 outcomes player 1 would win 18 times, player 2 would win 15 times, and they would tie 3 times.  The corresponding probabilities:  50%, 42%, and 8%.


At this point you could challenge the students to create a die that would always win.  I'm not sure that this is possible, but see where the students take you.  

Activity #2:  Create the Best Space Ship


You can find some information for this on Stone Librande's website.  Use this link, scroll down to 7) and click on Squoddron Odds Chart (Excel file).  This will lead you to all the possible outcomes but there are no directions.  That's where I will try to fill in.  

I decided to play against my son to make sure everything made sense.  So here goes nothing...

First you are going to need a 4-sided, 6-sided, 8-sided, and 10-sided die for each student.




Each student should draw a spaceship that has one engine, two weapons, and one shield.  Here is my spaceship:



And here is my son's spaceship:



Once you have your ships, place one die on the engine, one on the shield, and the other two on each weapon.  Which die on which part you ask.  That's the magic of this activity.  Each person gets to decide for themselves.  A person who thinks that the engine (or speed) is the most important will put the 10-sided die on that.  A player who things that offense is the most important will put the 10-sided die on a weapon.  You get the idea. 




Now you are ready to play.  You start this by decided who is going to attack first (you will take turns attacking each other).  Then both players roll their engine die at the same time.


We started with my son attacking me.  He used his 10-sided die for his engine and I used my 4-sided die for my engine.  He rolled a 7 and I rolled a 2.  Since he rolled a higher number than I did, his engine is faster than mine and he was able to attack me.  
Next he rolled both of his weapon dice (6-sides and 8-sided) while I rolled my shield die (10-sided).  He rolled a 4 and a 3; I rolled a 6.   Since my shield was a greater number than both of weapon numbers, I deflected both of his shots and he did not win the battle. 

Next we switched rolls.  We continued this back and forth until one of us won 5 battles.  At this point, the students would find another person to battle with, preferably winners vs. winners to have a class winner.  


Notes:

If the person attacking rolls a number lower than the defender, there is no battle because the attacker wasn't able to go fast enough to get to the other spaceship.    

If the engines roll the same number an attack will take place.

If a weapon and a shield roll the same number, the shot is deflected.

After playing a few rounds, I wanted to switch the position of my dice as I imagine my students might want to do.  This would be a good time to have discussions with them as to why they would want to change things around.  

BTW my son won.  












Saturday, August 2, 2014

Edugaming Workshop 2014 - A Reflection

Every summer two professors at the local community college hold an Edugaming workshop.  Mary Rasley and Steven Weitz received a grant from NSF to do this.  You can tell they are both very passionate about what they do and you can't help but be swept away with their enthusiasm.  They have it set up so that you work hands-on and listen to presentations for four days during the summer as you begin to create a game that you could use in your classroom.  A few months later we all come together again to present the games we created and used with our students.  But wait...there's more!!  Just this past year, the grant was extended (is that the right word?) so that their computer programming students would take our physical games and make them digital.  If you've been following my blog you are aware that I took advantage of this opportunity to have Bounty Hunter: Rise Up and Run become a digital game.

Monday, July 28, 2014


Today we had an excellent speaker, Stone Librande.  You can visit his website here, but I have to warn you, once you go there, you may never want to leave.  Stone seems to believe in doing to learn, and of course he was right.  We started the Workshop by playing games with people we barely knew.  However, after playing some games with them we formed a bond.  We knew each other's names, we were cheering each other on, and we were learning about game design.  If you are interested in the game Stone took us through, you can learn more about it here on his website.

He spoke to us more about game design and shared a few examples.  I left the workshop feeling inspired and motivated.

One image I want to share (thank you desmos) is what gamers call "Flow".  I created this image to share where you want your students to be, in the dark blue area.  If you have a student represented by the purple point, they're probably bored, the material is too easy.  A student represented by the orange point is frustrated, because the material is too hard.  But a students represented by the black point, is in flow.  This student is working on material that matches his skill level. Mr. Librande recommended creating games that grow with the student.  As the students' skills increase, then the challenge of the game increases and vice versa.



Tuesday, July 29, 2014


Stone was there to present in the morning session.  For this, he went over 19 Games in 19 Years.  You want to be inspired to create a game?  Listen to him talk about the games he has created.  Here is a link to 15 Games in 15 Years.  The writer of that article has listed some of the tips that Mr. Librande shared.  I looked at the faces of my cohorts as he was speaking and you could tell we were all in awe of what he has done and created.  If you didn't leave his presentation wanting to take on the gaming world, you weren't paying attention.

Here are some notes that I took:


  • Create games with your students
  • Make rules around the pieces
  • Give pieces personality
  • Create characters with special powers (ex. a witch who can put a time limit on another player)
  • Give players something to fiddle with when it's not their turn
  • Consider having two victory conditions (this or that)
  • Asymmetric rules and game (players have different rules)
  • All players think at the same time, then everyone executes at the same time
  • Technology is good enough to create your own game pieces
  • Design from a title
  • Let players "play" as themselves
  • Follow the fun (watch the players and notice when they're having fun)
  • Play-by-mail game
  • Make your own personal games, "I'm going to make a game to play with YOU."
    • Think small
    • Think long term
    • Challenge yourself


Since there were quite a few math teachers in attendance (almost half) he walked us through a probability lesson.  It was powerful to participate in this activity because we were asking each other questions that you would never see on a worksheet, we were having fun, and we were a little competitive.  Well, I was a little competitive.  I wasn't able to find any links to this activity on his website, so I will try to share what I remember from this activity in a later post.

In the afternoon we were led by John Nardone, an English professor at LCCC.  He walked us through a writing exercise and spoke to us about story elements in a game.  This was the first session where we were specifically asked to think about our game project.  We were encouraged to have a game that included a setting and a goal condition.

Wednesday, July 30, 2014


The morning session was led by Mary Rasley and Steven Weitz.  They have created a framework, or step-by-step model, to help us created educational games.


  1. Identify a specific concept to reinforce (very narrow)
  2. Analysis:  Break the concept into its component parts
  3. Consider the essence of the knowledge those components represent.  In other words, what is the meaning of each part?
  4. The essence becomes the core gameplay using the components
  5. Determine what the user experience (UE) will be.
  6. Build the rest of the game around the core.
  7. Refine the game through iterative play-testing.  
This session was great because they gave us some thinking time after the presentation of each step.  This allowed us to work on our individual games and refine it.

The afternoon session was lead by Jason Malozzi, a Mathematics professor at LCCC.  He spoke with us about the different probabilities in games and how this is important for balance.  Play-testing will get you past this but that is the looooooong way.  The one exercise he led us through was eye-opening as a game designer, even though I know all this as a math teacher.  Are you familiar with the game Yahtzee?  He asked us why they didn't include a pair in the game.  They have three of a kind, full house, small straight, and large straight, but no pair.  We started with some experimental probability, but the theoretical probably determine that with 5 dice a player would roll a pair 90% of the time.  Not too exciting.  This example is most likely obvious to many of us, but there are more complicated examples that are not.

I just want to point out that Mr. Malozzi was an amazing teacher.  He was funny, caring, and knowledgable.  If you live in the area of LCCC and want to actually learn some math, take one of his courses.  Just saying.  

Thursday, July 31, 2014


The first half of the morning session was led by Mark Barlet.  Mr. Barlet is the founder of Able Gamers.  Please take a minute to check out their website.  You will be truly amazed.  #includification

He can say anything better than I ever could.  Take a look at one of their youtube videos:






Saturday, July 26, 2014

Just Take Two #tki2014



I just returned home a few hours ago from the Keystone Summit, a week-long conference for tech-savy teachers in Pennsylvania.  It was quite an honor to attend this event.  First, your principal has to nominate you.  Next, you submit an application highlighting an activity or project that you used in your class(es) that was made possible only through technology.  I tell you this not to brag, but so you understand the caliber of the company I have been in for the last 5 days.

Sleeping in a dorm room reminded me of my freshman year of college, a great time in my life.


Something that stuck with me what the idea of walking away from the conference with two ideas.  What are my two take-aways from this past week?

My first 'project' is going to be creating an online resume.  No worries JT, I'm not looking to leave.  Digital portfolios were suggested by one of the speakers, Christine DiPaulo (@ckdipaulo).  I'm picturing a website that has tabs that correspond to the four domains of the Charlotte Danielson model.  I'll share once I have at least a skeleton of a website.

My second 'project' goes along with my last post with communicating with parents.  I would like to use Twitter with my students' parents, but I think more parents use Facebook.  I imagine a parent scrolling through their newsfeed and seeing a project that their child is working on in class.  What a great way to make my classes transparent.

Beyond my two projects, I've been inspired to lead at school.  There are changes that need to me made and I have a responsibility to act on these needs.  No longer can we as educators sit back and wait for someone else.  That someone else is you, it's me, it's all of us.  Stop waiting.  The changes that I feel are needed are better Professional Development provided by the districts and time to collaborate with our colleagues again provided by the district.  I need to be a catalyst for change.  But first I need a plan.  I have to sleep on this one....


If you haven't discovered powtoon.com yet, you might want to venture over there.  It's a great place to make dynamic videos for free.  I decided to summarize this post in a powtoon.  Check it out:


Saturday, June 28, 2014

Formal Observation Follow Up

I had my formal observation follow-up with my principal this week.  I like that we are asked to determine two areas that I need to work on for the following year.  Here is what we decided:

1) Questioning techniques need development to engage all students in using their brains to the fullest.


My first thought is to turn to my online colleagues and get their advice.  I'm looking for a book to read to help me in this area.  John Golden (@mathhombre) did suggest that I read Mosaic of Thought.  I will have to look into this more, it seems very interesting.



The universe works in strange ways.  Just as I was asking for a book to help me with my questioning skills, I received one....for free.  I attended a conference for the wrap up of a 4-year study on standards-based grading that I was a part of.  They gave each attendee a copy of Implementing the Common Core State Standards through Mathematical Problem Solving - High School. 



Hopefully by the end of summer, I'll have some good news for you on my new-found questioning skills.  


2) Explaining PARLO to families has dropped off since it is an expected practice and they are not shocked by it.  Continual efforts to promote proficiency based learning may help to expand it.  In addition, Mrs. Oswald and JTAHS will benefit by more self promotion of her numerous efforts and methods to help students learn.  


I have to admit, I haven't been communicating with families as much as I should.  To be honest, I think the only contact I had with parents this past year was if there was a problem.

Not only do I need to contact specific parents individually about their child, I believe I need to have something that is similar to a newsletter.  I'm thinking about a twitter hashtag that the parents, students, and I could use to have a whole group discussion about what is happening in class.  Maybe even setting up some twitter chats with the parents/students would work.  I can't get them to come in for parent-teacher conferences, but maybe I can get them to go to their laptop. ?????  Anyone try something like this?


Saturday, June 21, 2014

Global Math Department Stuff as Promised

If you weren't able to participate in the Global Math Department Webinar this past Tuesday (June 17th), you can still view it and see all the comments here.  Or you can see it below:





As promised in the webinar, here is the blog post that contains information on the games I spoke about:

The Line Game:

Here are the links that contain the materials you will need to play The Line Game, The Parabola Game, or the Sine Game.  





Domain Rangers:

Here is a link to the files.  This link also contains the next lesson that use in class after playing the game.



Here is a link to the video of me and Bob playing Domain Rangers.  I found that it's easier to explain while playing the game.  





Bounty Hunger:

I really don't have much information to share about Bounty Hunter at this moment.  The plan is to have something digital near the beginning of the next school year (2014-15).  Until then, we'll wait patiently.  

Monday, June 9, 2014

Okay Games Vs. Captivating Games

On Tuesday, June 17th, I will be conducting a presentation through the Global Math Department about the difference between okay games and engaging games.  I will also go through some of the classroom games I have created in more detail so you have something you can use in your own classes.

Right now I'm working on a blog post that will have all the documents for you to use based on the presentation.

I hope you can join us.  Tuesday, June 17th  9:00 - 10:00.

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.