This is easily one of my favourite problems that I have come up with.  Mainly because of the back story.  I handed a student this calculator, and he told me that it didn't work.  The numbers weren't working.  I showed someone else and they decided to throw it out, but I couldn't help but think that something more than broken buttons was the problem.

So ask the students: "What is wrong with this calculator?" or "What is this broken calculator going to give us for '433+233'?" 

Okay full disclosure here, this is not really what I want to give my students, but as a low tech version (and one that you can use as well), I have made these...

What I really want students to do is to explore their own numbers and find patterns on their own.  In order to do this, I want to program a base 5 calculator that kids can use on the school netbooks, BUT I don't know how to program.  If anyone has ideas about how I could put this calculator into my students hands without telling them that it is a different base please put them in the comments.

Update: The awesome Jed Butler programmed this amazing base five calculator on Geogebra. If you are not plugged into the MTBoS, you need to get on that!

The other option is I just put my calculator under the document camera and have students ask and record class wide.  That doesn't help you guys though, so this is what I have started with.  If you think I need some more/better examples please tell me in the comments and I will make them (groups of four look nice).

Update: I have also begun having students exploreJames Tanton's Exploding Dots. This is a great intro into different number bases, and really stretches students, but is not completely out of the range of grade seven students. So much love for this.

This is a pretty pure mathematics WCYDWT so I can only think of standard sequels. (Please give me more ideas in the comments, these are pretty lame).

• How does multiplication work in this number system?  Can you find some easy methods for solving basic multiplication statements?
• Pick a random base (2,7,12,4.5(?), 16), and create some problems, and share them with a partner.  What is different and similar among different bases?
• From @trianglemancsd How would you represent 1/2, 1/4, and 1/10 as a "decimal" number? What does 1.3, 1.021, and 0.033 become as a fraction? (All sorts of headaches happen here, clarify a fraction in base 10 or base 5; what does 1/10 mean?
• 
  

So this one hasn't done absolutely amazing on 101qs.com, but I think that the number of questions that line up together mean that I think we have a worthy entrance into the 3 acts database.

The most interesting aspect of this 101qs is not so much the commercial itself, but the outcome of the commercial.  The student that actually earned the number of Pepsi points to get the harrier and what happened to that.  So let's check it out.

So when I was a kid and first saw this, I instantly wondered, how much Pepsi would it take to get that Harrier? Also I always wondered, "How much more will it cost to get the Harrier via Pepsi rather than just purchasing it?" Youmight notice that the new version of this video (based on some comments) that I blocked out the points so that students can come up with the number themselves.  How could you offer this prize and still make a profit?

A couple of ways I would do this is have students look up some of these items to get a general sense of price to point conversion.  Then we can compare that to point to price in Pepsi.  This task is more about making reasonable decisions rather than finding the exact correct answer.

I am a bit worried about this reveal, because being right is always so much more fun, but seeing this we can talk about how completely unreasonable this deal is.  There is no way Pepsi would give away this kind of prize for so little. Enter the...

The whole reason I choose this task is that a 21 year old student actually came up with the points necessary for the Harrier.  These are some of the questions I would ask.

• You are a lawyer for Pepsi, trying to show that this commercial is clearly a joke, and not a real offer.  Prepare a statement for the judge.
• What is the least amount of money that the 21 year old could pay for the Harrier, assuming he purchased bottles and cans to obtain the points?
• Pepsi offered a deal, that you could buy a point for 10 cents.  How much could you get the Harrier for? (Yes this is an easy sequel for math teachers, but I know a few students that would have to think about it).

So a bunch of mathy people are going to be meeting up pretty soon here.  Yes, that’s right Twitter Math Camp is near, and since I am not going I wanted to give something to the blogosphere in solidarity.  Step one to this is creating #TwitterJealousyCamp for anything awesome from TMC that I simply must retweet.  The second step is creating this nifty guide that I have had in my head for awhile, but never found the time to write.  It is not so much for meeting at Math Camp (but may come in handy for some), but rather the “Hey let’s go for coffee, I’m in town” type of tweet ups. This guide is based mostly on true events. Without further ado, here goes...

Step 1 - Decide on a Meeting Location 

This is natural.  You want to meet, and assuming you are meeting in a real space-time type spot, then it is simple.  Choose your location, clarify it, double clarify it, and get there! Not much left to say here.

Step 2 - Ponder upon the Fact that you may be Meeting up with a Murderer

Remember when you (or your kids) first went on things like chat rooms (anybody remember those things? It was like Twitter, but in a ‘room’)?  You learned early on that anyone to whom you were talking was probably a serial killer, a crazy stalker, or some other predator.  Yet at some point, after you have set this meeting location, you realise that you completely forgot about your internet safety knowledge from the nineties.  A good time to remember these rules and ponder the horrors of what will most assuredly befall you when you meet @mathymurder is usually on public transit on the way to your meeting.

It’s all right though; I've thought through this for you.  Imagine a person goes through thirteen years of grade school and secondary school, and somehow comes out with the desire to teach.  Then this person goes to 5 more years of school to prepare to become a teacher.  They teach for a bit, become a blogger and member of Twitter only to lure other Math teachers into a Starbucks for a tweet up so they can bisect you?

Ya, I think that’s pretty ridiculous too.

Step 3 - Find Whomever You Are Looking For

So you have now arrived at your destination, and now you are trying to figure out if the person walking in your general direction is the person you are meeting.  You check their Twitter account and study every detail of it; you have memorised every aspect of their face, and now you know it is them.  Unfortunately, Twitter profile pics tell you absolutely nothing about what they look like.  Sure many people have a picture of their actual face, but that means nothing.  There is a very simple rule to follow when you are sitting there waiting for your tweep to show up. If you think it is them, it’s not.  The converse of this rule is also true; if you think they are not the person, they are.  Once you decide, one way or the other, the wave function collapses and you are wrong.

This scenario ultimately leads to sitting beside your tweep for fifteen minutes without realising.  If you want to avoid this, be very clear about who you are and when you arrive (I’ve been told that I need to let people know I look like a hipster, so now you know), or use this hilarious misunderstanding as the great ice breaker to avoid the inevitable and awkward...

Step 4 - Start the Conversation Somehow

… point that you realise this is a real person!  Twitter is not some fancy AI created by the Matrix to simulate real social communities online.  There are living people out there, and now you get to talk to them. Only this time, you can’t wait an hour to get just the right amount of wit, insight, and the always awesome meta hashtag to show that you rock at this communication thing.  Nope, now you have to interact with this person in real time.  Do you start with Math?  Do you ask what their favourite TV show is?  I don’t know what the surefire way is, but you’ve probably made a fool of yourself online so stop worrying about it now.  You’re only in this situation because this person thinks you rock, so just rock out!

Step 5 - If You HAVE to Do Math, Prepare to Fail...

I would almost say avoid doing math in front of your tweeps but let’s face it, that’s ridiculous.  We love math we want to do it, and we will do it.  As with any opportunity to do what you love in front of others who (at least for me) are better than you at this skill, you will inevitably make a mistake.  It’s hard I know, but this will happen.  The best part about it too?  It will always happen on basic arithmetic.  There’s no way around it.      

The best way I have found to deal with this situation (it really helps in every social situation when people put your numeracy skills into question) is to come up with a catch phrase to humourously explain away your folly.  Mine is “Oh, I’m good at math; I just suck at arithmetic.”  What works especially well with this technique is the conversation can be instantly diverted toward talking about how calculation and arithmetic is only one small part of the great world of mathematics.  This works to show that you really get "it," and also detracts from your inability to do the math that you probably penalise your students for forgetting (hypocrite!).  Plan B, practice your darn arithmetic!

Step 6 - Winding Down

So you have just finished your three hour long coffee, solved all of education’s problems, reminisced about tweets and blog posts of yesteryear, and now it is time to part ways.  Congratulations you have survived your tweet up, but you cannot forget the most important step.  The post-tweet-up tweet.  There are three important things you must remember about the post tweet-up tweet.

1. You cannot start the post-tweet up tweet, until you no longer have visible contact with the person.  Doing so before hand is like saying good bye to someone and proceeding to walk beside them for five minutes; it is always awkward.
2. Be polite and let them know how awesome they are. Don’t forget to mention any funny little anecdote that may have occurred.
3. Make others jealous!  I don’t think I have officially done such a thing before, but I know that whenever I read about tweet-ups I instantaneously wish I could be there, so I am assuming that this is an unwritten, but now written, rule of the post-tweet-up tweet.

And there you have it.  If you follow these simple steps you will have a great time meeting all those crazy people on the interwebs that have a fascination with this great and crazy world of education.  It’s good to know that I am in such fine company, and I hope you all know it too!