Hello Goodbye

You may not know it, but the Amazing Race is big in Canada. It is so big, in fact, that they are planning on running a Canadian version. I’ve already started training and I am currently accepting applications from people who would like to join me on the winning team. But I digress…

Last week’s season finale (season 21, I think) included a challenge that asked contestants to put banners containing the words “hello” and “goodbye” beneath country flags, in that order, and in the language from that country. The contestants struggled and the challenge took over 2 hours, but one contestant tackled it systematically by trying all possible combinations. It was made for a math classroom. In the WNCP, this fits Permutations and Combinations from Pre-Calculus 12 (Math 30-1) in Alberta. It also fits Math 30-2 in Alberta. Here it is, in 3 Acts.

Act I

Play the video by clicking the photograph of one of the contestants working on the challenge.

With any kind of luck, the students will wonder how many combinations of the “hello” and “goodbye” banners are possible. They will require more information.

Act II

This video is longer than the Act I video, and by watching it closely, they should be able to determine that they are working with 9 country flags, and 20 banners with words on them. There are 2 extra banners.

Act III

I don’t have a video with the answer. It is fun playing with this problem, though. Initially, there are 1,216,451,004,088,320,000 combinations (20 x 19 x 18 x…x 3). By getting France and Spain correct immediately, the contestants reduced that number by a factor of 116 280, and now only have 10,461,394,944,000 possible combinations to try. If they had truly had to guess them all, they’d still be at it.

Enjoy. Fix my math.

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Two Trains

In my school days, I remember (and not fondly) problems like:

A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto. The cities are 500km apart. The trains pass each other 2h later. The train from Montreal is traveling 50km/h faster than the one from Toronto. At what distance away from Toronto do the trains pass each other?

I’m no whiz with a video camera or script writing. I’m not much of an actor (which you’ll see if you bother to watch the video below). But I think this is a more compelling way of presenting the same problem.

Act I

Act II

http://vimeo.com/51113026

Act III

Answer

Sequels

I need some help here. Any ideas? Is it worth bothering?

• John was driving slower because he thought Darlene would drive farther to the meeting point. His plan is to drive 110 km/h all the way back, thinking that this would save him time overall. Would he have been better off driving 110 km/h the whole way?
• What if Darlene left an hour later?

Production Notes: My wife says that there’s no way I’d be that calm if I had to drive her purse back towards home.

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Surface Area vs. Volume

At a recent session in Wainwright, one of the participants, Mary Frank, showed me this demo. It’s similar to Dan Meyer’s Popcorn Picker, but I really like the payoff in Act III. Presented in Dan’s three act format, here’s the materials.

Act I – Video

Act II – Information

Have the students make predictions about whether the wider cylinder will overflow, fill right up, or have space left in it. If they want to run calculations, the tubes are simply 8.5 x 11 pieces of overhead paper. One is rolled vertically, and the other is rolled horizontally.

Act III – The Answer

Sequels

• How tall would the skinnier cylinder have to be to completely fill the wider one?
• By what factor are the volumes different? Why?

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101qs

When Dan Meyer launched his 101qs.com website in March, he invited people to upload first acts. I interpret Dan’s definition of first acts as compelling videos or photos that lead to perplexing mathematical questions. The idea of 101qs.com is for people to upload their first acts, and the other users will post questions if they are perplexed. If they are not perplexed, they skip it and move on. Each first act ends up with a perplexity score.

I spent a lot of time on the site in the past week, and have now seen every single first act that has been posted. I entered my question for those that perplexed me. I skipped those that didn’t. After all that work, I have some observations and questions.

Observations

1. What perplexes me doesn’t necessarily perplex you. This is my lowest scoring one. It’s busy. It’s text heavy. It’s cumbersome. And I’m totally hooked. I really want to check this guy’s math. Dud.
2. On 101qs.com, there are numerous similar examples of things that people found perplexing enough to upload, only to discover that the community of reviewers doesn’t agree. I wonder if perplexity relies at all on the presentation. I’m sure Dan would prefer that these things stand on their own; that the photo or video need no explanation or prompting. I am confident, though, that I could sell my dud in #1 to a group of students and get them perplexed. I am confident that Statler Hilton could sell this one to a group of kids with the right presentation.
3. Videos need to hook me fast. I have a short attention span that way. Apparently other people feel the same. This one is brilliant. Why it doesn’t have a higher perplexity score is befuddling me.
4. If I can’t tell what I’m looking at in the photo, I’m not perplexed. I’m confused. I wonder what the uploader wanted me to notice. That’s not perplexity. That’s teacher pleasing.
5. Simple is good. This one fascinates me.

Questions

1. Where does this go from here? Do we sort by course or topic related to the mathematics we anticipate students doing in Act II? Do we link them to Act II and Act III resources? What’s next, Mr. Meyer?
2. How do students react to these? Do they find the same ones perplexing that their teachers do? Some of the ones I have used with great success with students are not receiving the highest perplexity scores on 101qs. This one and this one have gone over very well in the classrooms in which I have tried them. Only one of them lives in the current top 10 on the site.

Pre-Emptive Reply to Your Comments

I know. If we have to sell it, it’s probably not perplexing enough.

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Amazing Watermelons – 3 Acts

I’m starting to see this stuff more places. This one could be fun. This one is easier mathematically than the Penny Pyramid that Dan Meyer describes here. In Dan’s 3 Act Format, here it is.

Act I

Video

Ask the kids what they wonder about. They could go lots of interesting directions with this one.

Act II

Video

This video will give them the information they need, assuming their perplexing questions require them to know how many watermelons are in the pyramid.

Act III

The Answer

The answer is in the form of a Word document with a photo and some calculations. I’d love a video. If anyone has the budget for 385 watermelons, the patience to stack them, and the video editing skills to insert a counter to the filmed stacking, I’d gladly take it.

Sequels

What is the mass of the pyramid?

What is the cost of the pyramid?

How many watermelons could we stack in this room?

If the truck is 20 m from the pyramid, how long would it take to build?

Any other sequels? If so, throw them into the comments.

Download

This zip file (29.7 MB) contains both videos.

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Safe Cracking in 3 Acts

I’ve been getting a kick out of the first season of this show.

Act I

Just to pique their interest, play this clip.  Ask them what they wonder about. Hopefully they talk about the number of possible codes.

Act II

Scene 1

Play this clip. Let them work.

Scene 2

Play this clip. Let them work.

Act III

I have no video that reveals an answer here. Let them share their solutions with each other. Then let the watch the clip below so they can at least find out if Fusco manages to get the file.

I may have learned a new trick. It’s possible that this link will take you to a zip file (10.2 MB) that will allow you to download all 4 videos. It’s possible that it won’t. Let me know, either way.

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The Lottery

I was in a meeting this morning, and we were discussing how to connect literacy across the curricular areas. I flashed back to high school, and a great short story we read. I started wondering whether I could use Shirley Jackson’s “The Lottery” in a math class. Then I began to wonder if a 3773 short story would fit with Dan Meyer’s 3 Act Mathematical Story Telling.  Here’s what I would try with this story.

Act I

Have students read The Lottery, by Shirley Jackson. Ask them what they wonder about. They will probably wonder about lots of things non-mathematical. Eventually they might wonder (Spoiler Alert!) what Tessie Hutchinson’s chances of winning the lottery were.

Act II

Ask the students what information they require to be able to answer the question. If they wonder how many families were in the first draw, you can have them look back through the story and count, or tell them that there were 16. They will also need to know that there are five members in the Hutchinson family in the second draw.

Act III

Students work it out. I still need to come up with a better way to reveal the answer, which is that Tessie had a 1 in 80 chance of winning the lottery.

Sequel

If this lottery has been going on all of Old Man Warner’s life, what is the probability that he survived to age 77?

Edit

Kendall reminded me that I started with connections to English class, and I meant to close with connections to English class. I would totally do this in collaboration with my school’s English teacher.

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A Billion Nickels – 3 Acts

I support mostly high school math teachers. I work with colleagues who support K-9 teachers. Last week, I eavesdropped on two of them as they tried to come up with a 3 Act Math Story in style of Dan Meyer that would apply to division 1 students. This week’s Parks and Recreation may have provided us with one. You be the judge.

Act One

Click on Andy to play the movie.

Act Two

Find out what the students wonder about and what information they will need to answer their questions. I suspect they will wonder whether it will really be a billion nickels. Depending on how young a group you give this to, they may need to know that nickels are worth $0.05 or that there are 20 of them in a dollar. Canadian kids may need to be told that those wacky Americans use paper for $1 instead of coins.

Act Three

The good folks over at Parks and Recreation didn’t film the right answer for us. If anybody wants to withdraw 20 000 nickels, stack them up in some way, film it or photograph it, and send it my way, I would appreciate it. Otherwise, this is the best I can do. Give them a photo and some information.

$1000 = 20 000 Nickels

Sequels

Could Andy hold 20 000 nickels? How much would they weigh? What size container would he need? Would they fit in his trunk? If he piled them all in a giant stack, how high would they reach? What about a billion nickels? How much would they weigh? How high would they reach if all stacked up?

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