This is Water

My school's graduation is two weeks away and I'm at home trying to write a speech for the ceremony while remaining calm. This is tough. The last time I gave a grad speech I quoted a bit from David Foster Wallace's excellent This is Water Kenyon College commencement address. I will probably draw from Wallace again, the piece is timeless. In the very small cache of documents I saved to bring back from India to New Hampshire there is a worn copy of the entire thing. I've probably read it twenty times, still gets me.

It turns out that a few days ago some folks turned an large chunk of the speech into a video. Click through the picture to check it out. Really great.

Click through to watch the video version of This is Water.

Click through to watch the video version of This is Water.

Here is a link to the full speech.

Crocodile Dentist

I get great review game ideas just browsing toy stores (and way way too many games). Crocodile Dentist was born this way. The game is sometimes hard to find, but seems to currently be available on Amazon.*

Gameplay is in groups, and nearly identical to Danger Cards, a review game I wrote about earlier. But in this one the croc is the star of the show, although the kids still do lots of math.

Croc1

Set Up

You will need the crocodile (obviously) as well as the Keynote presentation I use for the classes. I also print out worksheets for each round. Below is also the link to the Pages worksheet set I made for the lesson I ran this week. Most of the problems are snapped from Sullivan's Algebra with Trigonometry book.

Download Keynote
Download Pages WS

CrocWS

Game Play

Here are the rules straight from the presentation that I share with the kids, I've added a bit of extra explanation as well.

Croc2

At this point I jump immediately into the math by having the students work through the first page of questions. Teams hand in their worksheets as soon as they are done. Once most of the teams have handed in their sheets I cajole the final team into turning in theirs. During this part of the game I usually wander around the room making sure everyone is participating.

Once all the sheets are turned in I score them really fast and we discuss any questions that seemed universally unclear. I remind the kids before the game begins that this is primarily about review. Each team gets points for each right answer. The team with the most points goes first in the Croc Round and then play continues clockwise from group to group. (I've tried other turn systems but this seems to be the easiest for me to not mess up during the game.)

CrosTease

The Dentist Round works exactly as described on this slide. This is always intense because the winner of the round will nearly always be suspenseful, although the teams who were successful on the problems will have an advantage. To keep everything moving I usually only let one kid at a time come up to the table where the croc is.

Croc3

The bonus round immediately follows the dentist round. The winning team plays for candy.

Croc4

The round is nearly always a blast, because over and over again kids will take "one too many trips to the well" and not get any candy! It's hilarious. Further, if they manage to push four teeth successfully I usually start offering them deals encouraging them to press their luck (and get eaten) good times.

And that's it. Once the candy round is done we jump into round 2 and repeat. If you want you can keep score and have a grand champion at the end, I sometimes do this but it's not really needed. At the end of class I direct students to a Google Doc where they can access all the problems and solutions for additional review. This review game is a blast. If you give it a shot in your classroom let me know how it goes.


Links to Amazon.com are affiliate links when reasonable.

Danger Cards Remix

The other day my seniors, who are reviewing for their IB exam, wanted to play the Danger Cards game for a review session. I told them they if they made it, we could play it. Here is what I did.

danger pic 1

I quickly reformatted my Keynote slideshow to a Google Doc Presentation. The Danger Cards presentation is not fancy or anything anyway so nothing was really lost in the transition. I retitled the question slides with student's names and added blank answer slides after each question slide. Each student was responsible for creating one question slide and completing the subsequent answer slide. At this point I shared the Google Presentation with everyone in class giving everybody edit rights.

I told students that the slide deck needed to be finished by the night before we were going to play the game in class so that I would have time to choose the final set of questions we would use. They were also on the honor system not to cheat and study the questions (or more importantly the answers) their peers had written.

danger pic 2

Although the questions the students came up with were not in any way earth shattering, and the formatting of the slides was not as beautiful as it could have been, for a lesson developed in less time than I have spent writing this post about it, it was definitely a success. Students also had a solid bank of questions and answers (including many we did not get to use in class) that they could use for additional review.

Here is a link to a Google Presentations version of Danger Cards you can make a copy of and use with your classes if you want to try this activity out. Check out the original Danger Cards post for more details about the game.

Scaffolding Trig Graphs - Desmos Kong

Yesterday evening, way too late to be planning a new lesson I was noodling through Sam Shah's filing cabinet looking for something that would allow students to practice trig functions, ideally kind of game like. There is good stuff there, like this graphic organizer from Mimi, but nothing like what I was looking for. For years, here and there, I have heard people mention the graphing game Green Gobs but I have never actually used it myself. Still, downloading software for all of my students to use (that had to be purchased) was going to be out of the question, at least last night. Maybe I could make something similar with Desmos. I have been using Desmos more and more with the kids and loving it. A little while later I came up with Trig Scaffolding.

Anyway, let's get into it. The activity (1) I created is called Trig Scafolding: How High Can You Get? The entire thing is built into one Desmos worksheet. I demoed the activity for my students on the big screen and then shared the link.

I think this is all best explained with screen shots:

pic1

When students open up the Desmos Link they see the points of the function they are trying to graph.

pic2

Students know they are right if their graph matches up with the points.

pic3

The kids can «climb up» to the next graph by turning off the graphs they were working on and turning on the next ones.

pic4

I added notes along the way in Desmos to mark students progress and remind them about Desmos's excellent features like the easy integration of sliders. I spent the entire activity circulating and working with pairs of students. I was impressed with the total engagement the kids had through the block and the different strategies they were using to figure out the graphs.

pic5

No one picked up on the very thin Donkey Kong theme, but overall the activity worked really well. A couple groups did engage in some mindless guessing and checking, but most of the kids were really trying to reason out the functions with Desmos along with pencil and paper or whiteboards. Although I didn't do so, it would be easy for students to turn in their «solutions» for this assignment by having them save their graph and sharing the link with you.

pic

I was really unsure how difficult kids were going to find this when I created it, but the scaffolding of the problems seemed to be decent. It is easy enough to adjust anyhow. I think in the next iteration I will add more problems where I place restrictions on the graph, either to make the problems more challenging, or increase the level of scaffolding.

Have you tried anything like this with Desmos? I would love to see it and hear about it!


(1) I called it a game with my first class yesterday and the kids kept comparing it to other games like Danger Cards, I called it an activity in the other classes and there was none of this nonsense. In fact in the other classes the kids told me that it was «a good game!»

Save Kelly!

Rory, who has taken this activity and sprinted with it, has been hounding me to write a post about its creation.

survive

(1)

At my last school with the encouragement of my colleagues I picked up the physics classes when the physics teacher retired. My first year I did a lot of lousy book labs although I did manage to do the mousetrap car thing. I knew that moving forward I wanted to add more engaging activities for each topic we examined.

The Save Kelly activity was the result of my sister coming home from college and telling me about some fun stuff she had been doing at college in her engineering program and how maybe we could turn one of the activities into a lesson connecting to Newton's Laws that my students had been studying.

The activity works like this. First students are told the ridiculous back story. That is, they are out hiking with their friend Kelly (2) when suddenly Kelly is abducted by a vicious Pterodactyl and dropped on the other side of an expansive ravine. The students of course must save their friend. All the students have to save their friend is a survival kit, and some pennies. Everyone knows Pterodactyl's can be taken down with pennies right? What follows is from the worksheet I gave the students


Save Kelly!

As you are painfully aware your dear friend Kelly is being held by a vicious pterodactyl across the ravine. You gather your wits and take in the surroundings, first you pull out your survival kit and then you also notice two threads stretching across the pit. You figure that if you can transport pennies to Kelly, they can be used to do away with the pterodactyl.

Instructions:

Your group must use only the materials provided by the survival kit to design a system to transport as many pennies as possible using the twine. You may not use any tools (scissors, knives, etc) only what is in the survival kit, plus one meter of masking tape.

You may design your structure any way you want. With a couple of rules:

  1. Your contraption must start from rest at the designated spot. Once your contraption is set into motion it may not be touched again.
  2. The masking tape must not touch the pennies.

If you find you are running low on supplies you may barter with other teams. You are allowed to run trials, but take care not to squander your survival kit.

The Competition:

15 minutes before the end of the block two official trials will be performed; your rank amongst teams will be based on your best trial. Your score will be determined by the distance your contraption travels in floor squares, multiplied by the number of pennies you transport the entire distance.

The Write Up:

This activity will be written up as a lab report in your lab notebook.

Your write up must include the following components:

  • the necessary pieces of a standard discussion (reread your lab reports guidelines page)
  • sketches of your groups’ final design
  • a clear connection between the activity and each of Newton’s 3 laws as well as any other pertinent physics topics.
  • the results of the activity and how your team worked together to overcome challenges.

You have some options for the format of your lab write up:

For a maximum grade of a good solid B you can turn in a traditional lab report with only the discussion section (and of course the title, page numbers, table of contents, etc.)

For a maximum grade of an A you can turn in an alternative lab report. This written piece could take the form of a news article, a narrative (perhaps from the pterodactyl’s point of view), a journal entry, or something else.


The write up's for this activity were always awesome. A million times more enjoyable to read than 60+ (nearly identical) dreary lab reports. Here is a picture of one I saved.

obit

Overall, it's a pretty good activity, if you are teaching physics definitely give it a shot with your students.


(1) The survival kit basically contained what me and my sister found on a romp through the grocery store, with with some candy and red herrings like penne pasta, manicotti, and marshmallows. It also included a straw and some balloons. Rory put rubber bands in her survival kit as well, but I didn't use to. To make the bags I fed them though my inkjet, which although was probably a dumb idea for the printer, made for some awesome props. Props are huge.
(2) The first year I did this I had a student named Kelly. In future years I always implied Kelly was Kelly Clarkson. Which meant I could play «Since You've Been Gone» over and over again throughout the entire lab. Good times.

Induction by Contradiction

So for years I used Proof By Induction, but never really understood why it worked. This frustrated me, and so I set out to discover the «proof» for proof by induction. I searched far and wide in all my textbooks and just kept finding the domino analogy to justify the three steps. Sure the analogy is memorable, but to me it never seemed like a proof. So after looking up induction in nearly every book I have, I found a decent explanation in Paul Foerster's Precalculus. He uses Proof By Contradiction to develop induction and the method is both clear and logical. Unfortunately this great induction lesson has been relegated to an appendix, and there are no exercises at all (particularly unfortunate since Foerster's claim to fame is his problem sets). I used Paul's explanation to create a lesson, along with problems, and I have attached both below. I'm not teaching induction this year, but induction came up in a conversation I was having with my friend Bryan who is. The worksheet below is updated from the first time I taught this four or fives years ago. The last two times I taught induction, however, I turned the worksheet into HW problems to fit my Exeter style problem sets, these, and a whole strand of induction problems I used in subsequent problem sets are included here.

Induction

Passion, Trigonometry, & Locked Doors

The other day Rory posted a new problem solving method with a 75 letter acronym. I have no idea what it was, but the first letter was this.

P: What problem in my local community ignites my passion to the point of action?

On Friday at school I had a long conversation with John, a programmer who is working with ASB to design some gamification stuff. Looking around my classroom he saw the unit circles everywhere and exclaimed his love for trigonometry. «I need you to come talk to my students!» I exclaimed after he went on and on about how he uses trig all the time in the programs he writes. I wonder if he learned most of that trig when he really needed it for the coding, or it was all from tenth grade (I suspect the former).

chinup

Just like today when I finally learned how to break open a locked door with a credit card. I was standing in the doorway above, admiring my newly installed chin up bar, thinking «maybe tomorrow I will be able to do one chin up» when I closed the door to discover two things: first, the door could still close with the chin up bar in place (this should have been obvious) and, second, the door was now locked!

With no key, and a lock that was real (not one of those US bathroom locks that comes with a pin) it was time to hit the net. I had, of course, heard of using a credit card to open a locked door, but always figured it wasn't really possible with a real door or with a real lock. Luckily my computer was not in the locked room, so off to YouTube I went. Gold immediately, with a young man (maybe 12) clearly demonstrating how to open his front door with a credit card. I watched it a few times until I was convinced that I too could get into my locked bedroom, and I did. Here is the clip. John's desire to learn trigonometry was ignited by his passion for video games. I needed to learn lock picking to get into my bedroom. When passion is ignited learning follows.

TPIR 05: Safe Crackers

I have mentioned before that I am a huge fan of The Price Is Right. I wasn't always a huge fan of the game Safe Crackers though. I can remember watching TPIR as a little kid and being scared when Bob would walk towards the big doors at the back of the set. Frequently when this happened the doors would open to reveal Safe Crackers (and the terrifying?!) Pink Panther Theme.

I am, thankfully, no longer afraid of Safe Crackers, or Henry Mancini, but Safe Crackers remains a great pricing game to analyze. Since I like to introduce problems before math formulas I would definitely use this before I taught students about permutations. The kids usually have no trouble figuring out that the lock has 6 possible permutations and that only 4 of them are really viable. Occasionally a couple of students do even better. Here is what I share with the class.

safe_pic

Here is a link to the You Tube clip

The Price Is Right is the longest running game show on American TV, part of its lasting appeal is due to its wide variety of pricing games. Many of these games can be analyzed with probability theory. Take a look at Safe Crackers. What is the probability of a contestant winning this game? What about a Safe Crackers aficionado?

When we do our math homework on Google Docs (to prepare for discussion the next day) students write each notes back and forth on the document (and I chime in as well). Here are some notes they wrote about this problem:

PS_pic

Egg Hunt

Easter was my favorite holiday as a kid because we would always have these sick Easter Egg hunts at home and then again at my grandparents' house. My parents even managed to hide Cadbury Eggs for me and the sister when we were in the desert in the middle of Morocco one spring break.

egg pic 1

Cue one of my favorite non-math classroom events (1). Today before school I made it to the classroom early and hid about 20 plastic eggs (2) for the students to find. I stopped putting candy in them years ago, because students never find all the eggs and candy forgotten for months causes problems. We have the hunt at the beginning of class and then at the end of class the kids hide the eggs for the next group.

The students get really clever with their hiding spots and we always try to come up with seemingly «impossible» places to hide the eggs. Every class wants the class that follows them to find less eggs than they did of course! There is an egg, that never gets found, inside the Rubik's Cube on this alphabet poster for example. Good times, and totally worth the 10 minutes or so of class time this sacrifices. Happy Easter.

egg pic 2


(1) I have considered putting equations in the eggs and other such schemes to work math into this lesson but so far have kept it a simple hunt.

(2) If you don't have a set of plastic eggs (and who doesn't?) now is a perfect time to buy them because they are probably virtually giving them away at Walgreens and other such stores.

A Trig Assessment

Ever since Daniel started his series on assessment a couple weeks back I have been meaning to post some questions from my own assessments. Here is a one from a quiz we took in Algebra 2 with Trigonometry on Friday.

quiz pic

Proofs are difficult for students in general. What I particularly liked about the second part of this question was that although we had been talking about various trig identities created by the unit circle and the unit circle itself for a few weeks (see the previous blog posts), this important identity hadn't come up. I was saving it for the quiz.

I like giving students questions like this on quizzes because they challenge my students do more than just regurgitate some facts that they have previously memorized. Khan Academy can assess knowledge of basic facts (and simple applications) pretty well. I want my students to be faced with questions where they don't necessarily know what to do, and they might even take a wrong path.

This reminds me of Andrew Wiles' comparison (1) of mathematics to the exploration of a dark mansion

«one goes into the first room, and its dark, completely dark, one stumbles around, bumping into the furniture, and gradually you learn where each piece of furniture is, and finally after 6 months or so you find the light switch, you turn it on and suddenly it’s all illuminated you can see exactly where you are.»

Now, this proof was not Fermat's Last Theorem, but I think it was still challenging. My kids, of course, really hate that I put questions like this on their quizzes and tests at the beginning of the year, but they grow to appreciate them. And boy are they excited when they figure them out. They know, of course, which questions are the ones making them think. Here is a bit of their work.

quiz pic2

A second,

quiz pic3

These really exceeded my expectations, I was thinking maybe a few of my students would get the question right but it was a much much higher percentage.


(1): If you haven't seen this documentary about the Proof of Fermat's Last Theorem from BBC's Horizon program go watch it –really awesome. I always show it to my kids when I get a chance.

Automating Our Jobs Away

Interesting article with lots of good links from Quartz via NextDraft about how middle class jobs are more and more rapidly being replaced by computers. And in the case of the example below, the jobs that are left are being run by computers…

«In a gleaming new warehouse in the old market town of Rugley, England, Amazon directs the actions of hundreds of “associates” wielding hand-held computers. These computers tell workers not only which shelf to walk to when they’re pulling goods to be shipped, but also the optimal route by which to get there. Each person’s performance is monitored, and they are given constant feedback about whether or not they are performing their job quickly enough. Their bosses can even send them text messages via their handheld computers, urging them to speed up. “You’re sort of like a robot, but in human form,” one manager at Amazon’s warehouse told the Financial Times. “It’s human automation, if you like.”»

I frequently hear some variation of the quote «Any teacher who can be replaced by a computer should be.» it is easy for me to fathom adequate online math courses with hundreds of students in them. I think I could even teach an ok online math course to a large group of students. And what about if (or better when) Khan Academy begins offering certificates for course completion for courses such as Algebra 1 or Calculus and those students are shown to be as adept as the ones in the traditional classes? Maybe us math teachers will be replaced too. I think I have a job at least until June 8th.

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!