TPIR 02: Danger Price

Danger Price is another Pricing Game from The Price Is Right I have students analyze to learn about Probability. This one, like Flip Flop just requires students know the definition. Let's get right into it:

Click through to watch the clip.​

Here is another classic pricing game from The Price Is Right. Watch Danger Price and then use what you know about probability to answer these questions.
​(a) What is the probability of winning Danger Price if the contestant plays blindly         (i.e. just guessing)?
(b) Are there strategies a savvy contestant can use to increase their chances of winning Danger Price?
(c) The actual probability of winning Danger Price based on historical data is .361. What does this imply about your answer to part b?

You can get 40 years of pricing game stats here.​ Freaking awesome.

A few more Danger Price plays from the TPIR Web site.​

Shining Eyes

Today Daniel was ranting about ​teacher's who blame the students using the banned word they

“They don’t do their homework”

“They don’t take notes”

I remember my first principal Mark Roth saying some similar lines at one of my first ever faculty meetings. He continued to say he never wanted to hear his teachers saying  «they» when talking about students, it implied we weren't in this school thing together, and that the students were somehow separate and distant. We were making the students they who we would talk about instead of talk with. We would use words like we or us instead. This stuck with me.

​Daniel goes on

This is one of the reasons teaching stresses me out – because if my students are messing up, 99% of the time it’s my fault. Management issues? I need to add more structure. Comprehension issues? I need to tighten up my lessons. Retention issues? I need to change my assessment strategies. There are very few things that I can’t tie back to something that I can change about my classroom.​

​Indeed. It's why I can't sleep at night when class goes badly, like this past Thursday. And when I tell people this they think I am crazy. Seth Godin talks about how the leader is the one responsible for the success of the pupils a lot in Tribes*, but since my book is nowhere to be found I can't quote it.

There is another great example though. In his most awesomest of TED talks Ben Zander speaks about connecting with his students and knowing he is successful by looking for their shining eyes. You can't go wrong with this one.

Click through to Ben Zander's awesome TED talk about classical music.

*Amazon links are affiliate links.

Probability Faery Tales

To wrap up our recent probability unit in Math Studies I had my students write their own probability problems. For review at the end of «covering the content» students got to select a few options from a menu of rather lame probability worksheets I dug out from the filing cabinet. After this I had the kids create their own probability worksheet. I set this up with Google Docs and it worked great. I will see if I can summarize the process clearly here:

1. Students wrote their original problem and solved it.
2. Students posted their problem on a common Google Doc and posted a link to their solution on a separate Google Doc (this was so that students could solve all the problems that were created without being distracted by the solutions. This was their idea not mine. It worked
   
3. Students reviewed each others problems and solutions. They looked for possible mistakes, and offered feedback for improvement.
4. As the kids did all of these tasks they filled out a table on top of the Google Doc with the problems on it, this helped keep everything organized.

Here is a clip of the table student's creates. I showed them how to make links «pretty» using Command-K (or Ctrl-K) in Google Docs.

Here are a few of the problems the kids came up with.​

Noah's Clever College Worksheet:

In a fraternity of 90 frat boys, 48 of them like sports, 45 of them like rap music, and 20 of them like to play Pepsi pong. 12 of the boys like to play sports and like rap music, 9 of the boys like to play Pepsi pong and play sports, and 2 of the boys like rap music and Pepsi pong. Surprisingly, no Frat boys partake in all activities.
One day the school dean became concerned with the level of safety of each of the boys and how many activities they were partaking in, so he decided to survey the level of intensity of each frat boy.
(A) Fill in the Venn Diagram
(B) How many Frat boys like all three activities?
(C ) How many Frat boys like only sports?
(D) How many Frat boys like only Pepsi pong?
(E) How many Frat boys don't participate in any activities?
(F) How many Frat boys only like rap music?
(G) How many Frat boys like only one activity?

​This one was edited slightly for content but not where you would expect. This problem created lots of interesting debate in the discussion board before Noah added the line «Surprisingly, no Frat boys partake in all activities.»

​Nikita's Two Way Table Practice

One day Mr Roy walked into his room to find that the pillar in his room had been magically transformed into a hollow tree! When he walked inside, a voice (that may or may not have belonged to Gandalf) asked him to choose between a life-time supply or Petit Ecoliers, or Pepito’s. Of course, Mr Roy being the generous person that he is decided that he would ask his students which they would prefer so that he could share. Here are the final results of his survey:

Prequel: Knowing that Mr Roy surveyed 37 people, create you own Two Way Table.
(A) If one person was selected at random, find the probability that they love Petit Ecolier.
(B) If one person is randomly selected, find the probability that they hate Pepito
(C) If one person was selected at random, find the probability that they love both Pepito and Petit Ecolier (who can blame them?).
(D) If a person was randomly selected, find the probability that they hate Pepito or hate Petit Ecolier.
(E) If a person was selected at random, find the probability that they love Petit Ecolier, given that they love Pepito.
(F) Looking at Mr. Roy’s results, which were preferred: the Lu or the Pepito the winners?

​I love this problem because it employs a two way table with conditional probability. And, of course, because Nikita littered it with references only our class could love. My classroom has a large column by the bookcase and occasionally we have discussed decorating it like a large tree. The students are also keen on hollowing it out into some sort of fort. (I try to remind them that this is a support column, but they will have none of it.) Nikita also mentions our recent discussions of the virtues of Lu's delicious Petit L'Ecolier biscuits and the new to me Pepito cookies. When I mentioned in class my affinity for Petit L'Ecoliers the students insisted I had to try the Pepitos and so they brought a bunch in. Pepitos (not available in the US I don't believe) are delicious as well!

Finally, Ben wrote a very snarky probability problem that involved my (most likely) demise at the hands of either the big bad wolf or the witch. I reworded the problem slightly, swapped Ben for myself and put it on their probability quiz.​

Ben's Walk In The Woods

Benjamin is walking along through the woods dodging Easter bunnies and flying carpets. After a while he came across a clearing, in the middle of which stood large house made out of gingerbread and covered with delicious treats like Pepito and Petit L’Ecolier biscuits. As he cautiously picked his way across the lawn made of treacle he heard a wolf give a howl of sweets. As he approached the door, an old woman opened it. The probability that he runs away screaming is 0.2 should he run away screaming his chance of getting caught and subsequently eaten by the wolf is 0.1. Should Ben foolishly decide to enter the house his probability of getting eaten is 0.9.

(A) Draw the tree diagram for this problem and label the probabilities appropriately.
(B) What is the probability that Ben survives this unfortunate situation?
(C) Given that Ben was eaten, what is the probability that he decided to enter the house?

​Like I said, I was really happy with the way this activity turned out. It didn't take any more class time than usual and the kids had a blast writing, solving, and peer reviewing each others work. I need to do more of this.

Trig Speed

After my students measured the Unit Circle using the worksheet I adapted from Riley. We spent a class period or so figuring out all of the «nice» coordinates around the circle. A few kids vaguely (to my dismay but not surprise) remembered special right triangles, and so I made sure that we (mostly students at the board doing the heavy lifting) derived these from scratch. Once we filled in the coordinates all the way around the circle. I also introduced them to angle measure in radians and had the kids work in small groups to find all of these. This was fun because different groups were developing different strategies to figure out the angles and the room was buzzing with the discovery of new new strategies and approaches. Once we figured out all the angles we went through the entire diagram again from scratch and I asked the students to spend a few minutes seeing if they could figure out strategies to reproduce our unit circle quickly since next class we would have a quiz.

The picture links to the PDF file.

The first unit circle quiz day is always a good time because students come in and I ask them if there is a new pop song they want to hear and they inevitably choose something obnoxious and this works out perfectly. This year one of the girls chimed in and said «Just play anything by Taylor Swift!» I could not ask for more. «I Knew Your Were Trouble» it was. ​The quiz works simply, students keep the worksheet facedown until the song begins and need to finish it before the song ends. It turns out «I Knew Your Were Trouble» is 3:40 seconds. More than enough time for the unit circle. Maybe even two.  

Maybe you are thinking «Why do I torture the kids this way!» Haha. Well I am not out to torture them. I tell them straight up I am preparing them to be trig experts in the IB (that they will pursue next year) and that being able to quickly produce this unit circle will get them great results. Every year students come back from previous years to tell me how much it helped. And the students find it fun. I do give the students a grade for the assignment, but not until the third time through (unless they think they finished it) and their low grades can be straight up replaced as students can finish the task. After each daily quiz I have students partner up with a peer to figure out errors and strategize, and then if necessary we work together as a class to clear up any class wide concerns. I encourage everyone to try to improve their score. If you are now thinking «Well why would you memorize anything?!» Then I suggest this great article from Wired back in 2008. ​

I still, of course, haven't brought up the idea of cosine and sine, but students are more and more mentioning SOHCAHTOA and I am more and more insisting they must mean CAHSOHTOA.

TPIR 01: Flip Flop

I can remember watching The New Price is Right with my grandmother way back in the 70's and perhaps that is why I still love it today. Anyhow, I have found TPIR to be fantastic for engaging my students in probability and hooking them into analyzing some pretty complicated probability problems. Sometimes we analyze these clips in class, but frequently I just mix a TPIR question in with their homework. Going forward I am going to pretend that all these TPIR questions are from homework problems. I almost always assign my math homework on Google Docs. Every night students get a new Google Doc with a variety of problems on it, many are Exeter style problems, but I have found other problem styles (like these TPIR problems work really well on a Google Doc also) If I am really playing my A game the problems will be completely spiraled (like Exeter) and my students might get say 1 or 2 probability questions a night over multiple weeks until we have unwittingly learned a ton of probability. At Exeter math students can all meet in the evening to collaborate on their math homework (the Exeter math books even talk about this). At day (not boarding) schools this is usually not possible. This is why Google Docs works so well. Students go online in the evening and «talk» about their math homework on the doc. So after watching this probability problem I would expect my kids to begin analyzing it. We would then continue the discussion in class.

Click through to watch the clip.​

I bet we can learn some Probability by analyzing the world's best gameshow The Price Is Right. Let's start with an easy one. Watch this pricing game called Flip Flop and then answer these questions.
​(a) Are their any strategies a savvy contestant can use to increase their chances of winning this game?
​(b) What is the probability of winning the game if the contestant plays blindly (i.e. just makes a wild guess)?

Teachers and Social Networking→

George Couros has a thoughtful essay about how the personal vs. professional debate as it concerns teachers and social networking might be better reframed as public vs. private.​

For example. let’s say a student wrote about how much they hated another student and started bullying them online.  Does it matter if the student said, “well this is my personal account”?  Even if the student wrote it in a “private” email, it can become public with a quick screen capture and shared with the world.  To me, anything that is posted online, you should consider “public” no matter what your “privacy” settings are.

​The endless Facebook debates seem to have died down at my school, but everywhere I go Facebook is a hot topic of conversation. My general rule of thumb is to not post anything on Facebook I wouldn't want my mother to see. And since my mom is one of my Facebook friends this rule is grounded in reality.

Facebook, Bullying, & Anonymous→

Great article today from «The Atlantic» about online bullying.  

After a quick search by Sullivan, the blurry photos I’d seen many times at the top of the Let’s Start Drama page appeared on the screen. Sullivan scrolled through some recent “Who’s hotter?” comparisons and clicked on the behind-the-scenes history of the page, which the Common Review Tool allowed him to call up. A window opened on the right side of the screen, showing that multiple reports had been made. Sullivan checked to see whether the reports had failed to indicate that Let’s Start Drama was administered by a fake user profile. But that wasn’t the problem: the bubbles had been clicked correctly. Yet next to this history was a note indicating that future reports about the content would be ignored.

We sat and stared at the screen.

Willner broke the silence. “Someone made a mistake,” he said. “This profile should have been disabled.” He leaned in and peered at the screen. “Actually, two different reps made the same mistake, two different times.”

​When I talk with my students Facebook comes up all the time. Sure it's not usually about bullying but sometimes it is, and they appreciate it. The problem described in the article has happened to one of my students. We wrote to Facebook twice about the fake page that had stolen his identity and scraped pictures from back in MS, but it's still there.

Gator Golf

I love review games. Occasionally in high school I got to plan review games for my classes and it was awesome (I know, I know I am wicked lame) Anyhow, I think I first heard of using Gator Golf for a review game from the book Rookie Teaching for Dummies but I can never leave well enough alone so here is my twist on it.

Setup:

Divide the kids up into four teams -do this any way you see fit. Give each team a portable whiteboard to write down their final answers, along with scrap paper and golf pencils (obviously) to make notes if necessary. You will also need to get the Hasbro game Gator Golf. I also went to Home Depot and got some putting green carpet, and some tees and a putting glove at a golf store, you could probably make due without these but I love little details. Dividing class into groups and giving each group a whiteboard is a strategy I use again and again for many review games and it works pretty well.

The Game

The game is played in multiple rounds

Round 1:

This round relies most heavily on the keynote presentation (see link below). In round 1 there are 16 multiple choice questions (the questions I included are all about trigonometry). When a question is revealed each team answers it on their whiteboard and then "locks in" the answer by flipping their board upside down. Once three of the four teams are locked in I cajole the last team into finishing as well. At this point the answers are revealed. The team in «control» reveals their answer first followed by the rest of the teams. If the team in control answers correctly they score a tee, if not, the next clockwise team has a chance to steal, etc. After each question is finished control passes to the next clockwise team around the room, the team in control is indicated by the location of the alligator in the slide deck.

Golf Round:

After the 16 questions are up I tally the tees that each team earned to determine each team's golf position. Sort of like in Hole In One on The Price Is Right (another post for another day) The team with the highest score gets to putt closest to the gator (but not too close). I usually wait until after the scores have been tallied to reveal the gator which always goes over very well. Prior to this just the green is on the floor and so the kids' curiosity is piqued. Everyone gets one putt, they score one point for hitting the gator at all, and three if the gator devours and spits out their ball. It is really important to allow the kids to have some fun golfing while also not getting so bogged down in the golfing part that no additional math gets done. If you move swiftly you should be able to get through the golfing business in no more than 7 minutes or so. If your class is enormous, you might want to have only half of each team golf during round one.

Yash lines up for a put.

Round 2:

Each team gets a few minutes to peruse the longer form questions from the round two document (included in the zip file) then I have the teams in reverse order of score select a question (or two based on time) that they want control of. After this selection each team gets a few minutes to work together on their questions and write up solutions on the classrooms whiteboards (not the mini ones) for everyone else to see. If teams have extra time they can try to solve the questions their team did not select in hopes of stealing another teams questions. Once time is up I score each question, one putt per correct answer and we golf once more. This golfing round goes much more quickly since there are a maximum of 10 puts, probably much less.

Final Round:

If there is time, I will have teams wager part of their score on one final putt. To determine the grand champion.

I actually didn't give any of the teams any prizes for winning the golf game this year, just the glory of being champions. Candy would work fine but is not really necessary, I would certainly advise against giving any sort of bonus points as a prize.

Other Thoughts:

I hadn't played this game in a few years, since the first gator met his demise, but I saw a new release of Gator Golf recently and picked up a copy. The game takes a bit of work to set up but always goes over very very well. I love tweaking rules and things so am always changing the games around to try to make them better. This time for example I had red tees and white tees mixed in my golf hat and when teams scored a point during round 1 they drew their tee out of the hat, red tees counted double. 

Whatever you do with the rules be sure to tell the kids what they are ahead of time and stick to them, kids go crazy when you change the rules in the middle of a game. Also during round one don't hesitate to stop the game and "go over" the tricky problems. This is a review game after all.

I wish I could stage shots like this.

Files: This file includes the Keynote slideshow I used for round one. Lately when I am making a slideshow for a game I create a Pages document with all the questions to begin with so I have included that document as well. I also included a copy of the Round 2 questions. These are both in PDF form also. The questions for this game are all about Trigonometry covering through trig equations but the game can easily be adapted for most other topics. 

*If I link to something for sale on Amazon it will most likely be an Amazon Affiliate link. Maybe someday these will pay for the blog (but as of this writing I have a click through rate of 0, which is not surprising because this blog is brand new, but anyway)

Measuring The Unit Circle & CAHSOHTOA

We started trig last week in Algebra 2. I began this time around with a trip online to see if I could find anything new to begin the unit with. I found this great post by Riley (via Sam Shah) about having kids measure the Unit Circle. A kind of sandbox approach. Anyhow it worked fantastically. In all three of my classes we were able to have great discussions about all the stuff that was learned by measuring this all out by hand. And I don't think anyone even asked «But Roy, when are we ever gonna use this?» In one of my classes the students got into a little debate reminiscent of Name That Tune's bid a note as they tried to lower the number of measurements that were actually needed to label all the points on the circle. I was sure they would figure out the various quadrants, but when they made the connections to the complementary angles within the quadrants I knew for sure this was the perfect activity to begin trig with.

First half of the first half of the worksheet.

Incidentally I took Riley's picture and turned it into a worksheet. Here is the file. I began class by having my students type their data into a Google Spreadsheet that I set up with them to calculate the mean of their scores. I plan on going back to this spreadsheet in the next couple of days and adding a cosine and sine value to it.

A couple of students know we are studying trig and have asked «Roy, does this have anything to do with SOHCAHTOA?» and I have been like «What is that? It sounds similar to CAHSOHTOA! Is that what you meant?»

First half of the second half of the worksheet.

A Good Place to Start

This is the Star Chart. It is always on the wall in the back of my classroom. 

Student's ask me questions about the Star Chart. Here are some things I tell them. «I have no idea where it came from The Star Chart has always been in my classroom, perhaps it is from... » «No, of course I did not make the Star Chart!» «Maybe, it is some kind of code!» «Yes, I would be indeed put out if the Star Chart were to disappear» -and the day that sassy comment was made was the same day that I snapped this photo.