Danger Cards

Sometimes I get to school and realize the plan I had for a class is not going to work. Or it will work but be boring for me teach and hence probably even more boring for my students to learn. This was the case a while ago in my IB Math Studies class. I was just going to have the students do some IB problems for practice. Normally I would tie a lesson like this to a review game, but I hadn't done so yet. Luckily I had a prep block and so I got to work.

I knew it would be a group style review game, something akin to Bazinga, a similar activity I hadn't seen until today when I started writing this blog post. Groups would complete a question and draw a card. I also wanted the game to have some treachery, strategy (beyond answering questions), and cross team interaction. What if the cards frequently did bad things? Danger Cards was born.

DC1

The first version pictured above definitely looks like it was schemed up during prep before class. Happily, I've tweaked the game through 4 or 5 iterations over the past couple months with various classes and the current version is solid.

I used Illustrator to design envelopes for the cards. With magnet tape they stick to my whiteboard.

DC3 - The Envelopes

And I designed a matching keynote presentation you can download and edit for your classes. I used off the beaten path fonts in this one, so the deck you download will probably look different than mine. You can just change the fonts to work with ones you have.

DC4 - The Keynote

Set Up

You will want to either make your own envelope decals or download the ones I created here. The labels are in PDF form but completely editable in Adobe Illustrator. Also download the Keynote linked above. Finally, you will want to create a set of index cards to put in the envelopes. You can use my current set pictured below or make your own. The Bazinga post I linked to has some great ideas for stuff to put on the cards as well.

DC2 - The Cards

Game Play

Here are the rules from the first slide of the presentation that I share with the kids, annotated with a bit of extra explanation.

  • Work with your team to solve the problems on each slide.
    • I try to make teams of 3 to encourage everyone to take an active role.
  • Work in your notebooks and then put your final answers on the whiteboard.
    • Everyone writes down the problems and solutions –again to encourage everyone to take an active role.
  • Deliver your whiteboard to the answer box.
    • The answer box is just a plastic bin that normally holds paper for recycling.
  • Once all but one set of answers are in the answer box, the round is over and the last set of answers must be turned in.
    • Not as hard and fast as it sounds, if a group is working hard, I'll give them leeway.
  • Highest Score (by order turned in) chooses a card and views it.
    • They need to be careful not to show their hand! This part of the game makes it really awesome because the kids come up with all sorts of ridiculous strategies to try to fool their classmates.
  • Each team (clockwise) can choose to play or pass the card as well.
    • Again lots of strategy because teams need to try to figure out if they actually want the card that was chosen, and if they have already seen the chosen card (or if another team has)
  • Each team has one Z-Chip you can cash in to reverse any one decision i.e. to undo your «play or pass» decision or even «forfeit the card you chose»
    • So basically once in the game a team can take back a decision they made. The team that chose the card can also take advantage of this, although the card still effects any team that chose to «play» it. The decision to play or pass a card must happen before the next question round begins.

Before we start the first round each team chooses a Danger Card and gets to «peek» at its contents before it is returned to the whiteboard.

The Cards

I think most of the cards are obvious but here are explanations of a couple of the tricky and unusual ones:

  • Peek - Cards that say + Peek allow the team that chose the card to peek at another card of their choice at the end of the round.
  • Treasure - Cards that say + Treasure allow the team that chose the card to grab a prize (usually food) from the Treasure Chest. The Treasure Chest is a, usually locked, wooden chest in my classroom. I brought it to school originally for a different (even more sinister) review game I'll talk about in a while, but lately I use it for many games. Kids love it when I open up the treasure chest for the first time.
  • Steal Another Team's Points & Swap Points With Another Team - Both of these cards create kind of a mess to execute, but so far I have stuck with them. Basically, the cards resolve in reverse order. So the team that decided to «play» the card last makes the first choice as to whose points to steal, the team that selected the card would resolve last (usually a huge advantage)

Overall

My classes are universally fans of Danger Cards, if you give it a shot in your classroom I'd love to know how it goes.

I found the skull picture from a quick google image search from here

TPIR 04: Freeze Frame

I love to use pricing games from The Price Is Right to teach my students probability. Freeze Frame, although it only involves basic probability, works well for this. Students are generally not exactly sure how many possibilities there are, and have to physically count them or make a list. Usually when we are discussing Freeze Frame as a class I talk about how difficult the counting of options in probability problems can frequently become. 

In prior posts I have mentioned how I usually flip these videos and have students watch them for homework on YouTube and discuss them on a Google Doc. For Freeze Frame I integrated it into a lesson and had students work out their solution in pairs on whiteboards. Everyone also made a «guess» as to the right answer which we finished watching after we talked about the problem.

Something else we always discuss with these Price Is Right problems is what the savvy contestant would do (frequently vs. what the average bear would do.) I mean sure, $1129 is one of the possibilities for the trip to Hawaii, but obviously the trip would cost much much more than that. If I have looked up the stats before hand it is also interesting to compare our best savvy contestant's probability to the actual probability of winning for contestants on the show.

Click through to watch a clip of Freeze Frame.

Click through to watch a clip of Freeze Frame.

The Price Is Right has male and female models now, and amusingly for my class the model in this clip had his shirt off. The Price Is Right Web site usually has about 5 different playings of each pricing game to watch, so if you like you can find a different playing of the game, but it is down as I write this.

Flip:

It's time for another fabulous pricing game from The Price Is Right. Watch this clip of Freeze Frame (stop the tape before the contestant chooses an answer, about 1:35) and answer these questions:
(a) What is the probability of winning Freeze Frame if you just close your eyes and pull the lever whenever?
(b) Being a savvy contestant you would, of course, not do this, other than deferring to the audience, how would you increase your chances of winning Freeze Frame. What do you estimate your probability of winning to be?
(c) What do you guess the answer is? Finish watching the clip to see if you were right!

The Pyramid Game

The other day, in a post about the lately very funny Family Feud, Dan asked

«Which game show works in the other direction, giving you lots of items and asking you to move one level of abstraction higher to the category that includes them?»

There are probably multiple answers to this question, but the most obvious answer to me is the bonus round from the $100,000 Pyramid, known as The Winner's Circle.

The game is best learned by watching a few You Tube videos (of which there are hundreds). But here are the basics. There are two primary players. One player gives the clues to six subjects of increasing difficulty and the other player is trying to guess the subjects that those clues fit into. The clues must be in the form of a list of items that fit the subject or category. So if the subject was salad dressings the clue giver could say «French, thousand island, or Italian» but they could not describe the category saying something like «It's what you put on a bowl of leafy vegetables.»  The clue giver is also not allowed to use charades, synonyms, or prepositional phrases. So, for example, for the category «Things that are quiet» «moviegoers» would be a permissible clue, but since «people at a movie» is a prepositional phrase it would get you buzzed. It's fussy sure, but that is what makes it great.

I have used The Pyramid Game as an occasional segment in my classroom since my first year of teaching. At the beginning it was very rudimentary:

Before I had a projector I played the game by holding up big index cards. I apologize about the Word Art. I was young.

Before I had a projector I played the game by holding up big index cards. I apologize about the Word Art. I was young.

The first time I played this game in class there was no YouTube so I actually spent a few days video-taping Winner's Circle segments at home, signed out a TV cart at school, and showed some clips during class. Today I would probably flip the introduction part and have kids watch a couple of the YouTube clips beforehand and then maybe show one more in class.

Click through for the clip. Great one because Billy Crystal is the Pyramid master. And because Dick explains the rules as well. This video seems to load slow, so cue it up ahead of time.

Click through for the clip. Great one because Billy Crystal is the Pyramid master. And because Dick explains the rules as well. This video seems to load slow, so cue it up ahead of time.

Students play in pairs and while only two students play at a time it is easy to get the entire class involved because, especially at the beginning, hardly anyone will win the game! After the group loses everyone else can chime in with the clues that were missed in the heat of the moment. The harder subjects can really get you thinking. A great strategy is to try to approach the category from multiple different directions. If the category was «Things that you join» you could try the obvious «a club» and then also «pieces of wood» (yes «of» is a preposition, but it is allowed).

There are a whole series of videos showing what not to do in the Winner's Circle. Great for teaching the game.

There are a whole series of videos showing what not to do in the Winner's Circle. Great for teaching the game.

Here is one of the first slide deck iterations. A student came up with the category pictured.

I thought this was pretty good at the time!

I thought this was pretty good at the time!

You can also tailor the game to your classroom. I am going to use this game at the end of class a couple days this week, so I will include categories like «Facts about the Unit Circle» and «Trig Identities.» The frequent TV show categories similar to «What Goldilock's Might Say» are also great for classroom use, «What Mr. Roy Might Say» is also usually a hit. Just like on Family Feud and Dan Meyer's clip if you open the door to racy responses the students will run right through it, you have been warned.

Students initially find this game extremely challenging, but also grow to really enjoy it (You might need to play it a couple times to appreciate this). I have had students get so enamored with the game they devise their own clue sets for classmates to try. They frequently go for the ludicrous «Things a Vegetarian would not Eat», «Bad Jokes», or the impossibly difficult «Words that Rhyme with Orange», «South Dakota towns» etc.

Dan's post inspired me to touch up my Keynote* slide deck so that it looked more like the classic TV show from the 80's and so that it would also be as easy as possible for someone other than me to use in class. The deck I am posting here has five rounds ready to go. There are also a few template slides at the end explaining how to easily customize the game for your classroom. Finally, I added a rules slide at the beginning to explain the game, but definitely show them some clips from TV as well.

Here is a screenshot of the latest iteration. Click through to download the Keynote slide deck.

Here is a screenshot of the latest iteration. Click through to download the Keynote slide deck.

*In a perfect world I would program this in Flash, but for the time being a slide deck works pretty well, you will just need an additional timer, and you can't really go back if the students pass on a subject.

Lesson Playback: A Trig Foldable

If I am not at the top of my game, my third algebra 2 class can be a challenge. I am usually able to finagle the schedule though so that my third class lands the day after I had a chance to teach a lesson in the first two sections and can hence make adjustments to it with them in mind. This can result in a class that can eclipse the quality of the first two.

Today I wanted to further consolidate our learning about the unit circle. There aren't really many blog entries here so it should be easy to catch up if you are interested. Last class we worked on the trig puzzle I created, most groups managed to solve it and many even worked out the quote. You know an activity is engaging when you get e-mails late at night proclaiming a solution or kids running into class doing the same. The six identities were more of a challenge. They would be today's focus.

Usually it's 5 Minutes of ❤.

Usually it's 5 Minutes of ❤.

Today instead of the normal routine we started class with a 3-minute brainstorm. I always time this stuff on my phone and the alarm is almost always the same song. Currently Eric Hutchinson's lovely Rock and Roll. When the alarm sounds the kids stop working and immediately begin singing along. Always, and no I did not tell them to do this, these traditions just begin. When I turn off the timer it is quiet again. After the three minutes were up I did a quick snowball activity. Basically all this means is the students crumple their paper up like a snowball (kind of foreign in Mumbai) and throw it somewhere else in the room. This is not my favorite activity but kids like throwing their paper at one another, and used sparingly (like once or twice a year) it works. Once everyone retrieved a new paper I set the timer to two minutes and had them add facts to the new sheet they had. After this round they passed their paper to a neighbor and added facts for one more minute.

Next I picked one of the front whiteboards (my classroom is a whiteboard paradise) and we did some rounds. I went around the room, student to student, and had each of them contribute a fact they thought were important to the whiteboard map. I scribed. In retrospect I probably could have had a student do this, although they were all busy adding facts they had still missed to their sheets. About halfway through this process I deadpanned that this was even more fun than Scattergories. Although it actually was fun, and everybody was engaged. With no classes up to this point resembling a traditional lecture, my kids had collectively figured out a lot about the unit circle.

Results of our group brainstorm.

Results of our group brainstorm.

With a board full of information I told my students to indicate on their papers the three most important points we had put on the board and look up when they were done. Next I got them out of their seats and had them indicate their selections using asterisks or checks on the board.

With a quick review of the unit circle over, it was time for arts and crafts. I had decided yesterday that I would try one of these «foldables» I endlessly see on math blogs, so we gathered round and Katie taught us how to make one of those fortune telling things.

IMG_1498.jpg

Back to the front I went. I surmised from the previous day's lesson that while few of the students had figured out all six (three pairs) of the trig identities I had included in the puzzle, we could probably come up with them in a group brainstorm. It went really fast actually. Our fortune teller foldable would house this information.

Quick sketch of what the final draft should look like.

Quick sketch of what the final draft should look like.

I split the kids into small groups for the next part of the activity that was a jigsaw. Each group had to sketch a diagram (with words if necessary) that would illustrate why their trig identity pairs were true. I gave them 9 minutes to come up with their diagrams and then each group presented to the others. During this time I moved from group to group to give advice and ask questions.

I had thought their might be a few minutes at the end of the block for students to fill in their foldables, but the block was about done. Students snapped photos of the whiteboards and will complete the task for homework.

Draft explanation of two of the identities.

Draft explanation of two of the identities.

So not the most exciting lesson ever, nor the review game I thought I was going to write about today, but a good example of a lesson on a day in ordinary time.

TPIR 03: Gas Money

Gas Money, which debuted in season 37, is one of the newer Pricing Games on The Price Is Right so you may not have ever seen it before. Although the probability of winning is basic, it is still an interesting game to watch because the contestant can walk away with the money if they choose to. The probability of winning Gas Money, is virtually the same as for Danger Price, the game I talked about last week. The thing is, when I used this game in class my students were all confused. They seemed to think that for some reason the probability of winning increased when cards were revealed. Like it was some version of the Monty Hall problem, a problem we had yet to discuss. The game is also interesting because the theoretical probability of winning is higher than the experimental, a fact I vaguely allude to in the questions but can be teased out more in class.

Click through to watch some clips.

Click through to watch some clips.

Gas Money is one of the newer games from The Price is Right. Watch a clip of Gas Money and then use what you know about probability to answer these questions.
(a) What is the probability of winning Gas Money if the contestant plays blindly (i.e. just guessing)?
(b) From season 37 through season 40 on The Price Is Right, Gas Money was won only 6 times and was lost 42 times. Explain why is this curious? What might be the explanation for this?

A Trig Puzzle

Generally reinventing the wheel is not the way to go with a math activity but I am a glutton for punishment sometimes. Years ago teaching pre-algebra I had made students a handwritten puzzle worksheet in which to solve they had to cut out the pieces and reassemble them into a box making sure to align the sides using exponent rules. This, I think, might have been inspired by a similar Pizzazz worksheet.

These ladies were on fire during this activity. Just outside my classroom are these awesome booths where students can work, love em.

These ladies were on fire during this activity. Just outside my classroom are these awesome booths where students can work, love em.

Anyhow, in one of my recent field trips through Sam's filing cabinet I remembered downloading something similar called a Tarsia puzzle. I would create one for my trigonometry students I figured. They had mastered the Unit Circle and I wanted to have them use the unit circle to have them think about some of the basic identities (odd, even, co-function etc.) I figured one of these puzzle worksheets could serve this purpose well. It might also be a nice bridge between the trig we had done so far and the next lesson I had originally planned about identities that I feared would be too hard. It turns out there is a free program to create these Tarsia puzzles (great resource here), but alas it is Windows only and at home I only have a Mac. Nevertheless the idea was gnawing at me so I decided to go for it and make my own.

I found the PDF I had downloaded from Sam's site (I can't seem to find the exact link) and opened it in Illustrator. From here I was able to delete all the original equations and add new ones I created in Math Type. Before I entered any equations into Illustrator I made a list of the six identities I wanted to focus on and made eighteen pairs that students would have to match. Next I drew the final shape for my puzzles' picture on paper and entered the equations to create the key. From here it was relatively easy to create the student version of the worksheet because I just cut up my key and entered my triangles into Illustrator. It was initially challenging to get the text rotated and oriented properly but by the time I had entered a few triangles of data I was a pro.  Additionally, I decided to add a couple layers to what was already a puzzle. First, I did not tell my students what final shape the triangles would be assembled into, and second I added a quote (that connects to the shape) that would reveal itself when the puzzle was completed. Further the quote has blanks that need to be filled in, making it even more challenging. I also figured that the blanks in the quote would make it more difficult for students to work the puzzle backwards. The quote also made it really easy to check to see if the puzzle was properly solved.

I've used this activity with two of my three algebra two classes so far and it has gone great. It is a little bit more difficult than I intended but in one class one group was able to crack the whole thing during the time allotted but just barely. Another group stayed behind after class to finish it. During the lesson I moved from group to group and helped students make connections between the puzzle and the unit circle, great lesson for a Friday afternoon math class.

Click through for a PDF version of the puzzle, editable in Illustrator if you have it.

Click through for a PDF version of the puzzle, editable in Illustrator if you have it.

Trig Speed Madness

So I am now about a week in, to what has become a mild case of unit circle madness here at ASB. I got the grand idea of posting students completed unit circle worksheets on the wall with their times and blocks when they completed the task correctly in under 3:40. The length of «I Knew You Were Trouble.» I had told students to say «done» when they finished the task so that I could tell them their time to write on their paper. Of course, on the first day of this I wasn't even looking at the time when at 2:10 or so Camille shouts that she is done, and she was, correctly. Up to the wall she goes. And it's on. Everyone wants to be on the wall, and everyone on the wall wants to post a better time than they did previously. It's not unusual to spot kids practicing their unit circles at break and lunch.

Completed Unit circles from C & E blocks. C block managed to have every student in the class successfully complete their challenge today!

Completed Unit circles from C & E blocks. C block managed to have every student in the class successfully complete their challenge today!

I encourage the students to compete against their personal bests and not against each other. But of course they do both. The fastest time I have ever ever seen goes to Malavika who has been killing it all week. 1:12 then 1:02 then 1:01 and yesterday an unbelievable 54 s. The entire class to a moment to gasp.

54s Wow.

54s Wow.

But that was yesterday. Everyday is great new fun with the kids. This morning I was in my classroom losing a fight with the school printer when I realized I was about 6 copies short of the Unit Circle quiz sheets I would need for class (that was, of course, about to begin). «Oh, I might be able to help you with that Mr. Roy» says Ruby from a few feet away. «Huh? You have blank copies of the Trig Speed form?!» «I might» she says. «Well do you have 6?» Indeed she does! «I made some to practice.» I am of course laughing, because this is both awesome and ridiculous, a hallmark of ASB. And Ruby achieved a personal best when she finished her unit circle in 1:57.

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.

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.

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 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:
Screen Shot 2013-03-01 at 7.56.42 PM.png
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 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.

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.