Same Problem, Two Presentations

In my quest for a good Three Act Problem for elementary level students, I’ve come up with two more ideas. It’s actually the same idea presented in two different ways. It’s going to hit division at the grade 3 or 4 level, I hope.

Hay Bales – Act I

Cars – Act I

These videos are rough. The car one could be fantastic if a car lot would let one of us come by with a video camera and film them loading a carrier. The hay bales one would be great if we could get a farmer to let us film him loading a truck. In the past week, I have driven to Calgary and back, Stettler and back, and Red Deer and back. I’ve seen a ton of those bales in fields. I haven’t, unfortunately, come across any of them being loaded up or hauled along the highway.

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69 Children

Here’s another attempt at an Elementary-style 3 Act problem. No photos. Just a story. I got this one from my 8 year old daughter, who likes reading the Guinness Book of World Records. This story fascinates her. In class, I’d read right from the Guinness site for Act I.

Act I

The greatest officially recorded number of children born to one mother is 69, to the wife of Feodor Vassilyev (b. 1707-c. 1782), a peasant from Shuya, Russia.

http://www.guinnessworldrecords.com/world-records/3000/most-prolific-mother-ever

Act II

Depending on what the students wonder about, you could go in some different directions here. My daughter wonders about how many of this woman’s children didn’t have a twin. In that case, the information to provide is that the 69 births contained 16 pairs of twins, 7 sets of triplets, and 4 sets of quadruplets.

Act III

The payoff here is that when students do the math above, they will discover that there was not one single case where only one child was born out of all 27 of the pregnancies. That fact makes the whole story seem suspect.

Sequels

• How would you know if the total number of children is even or odd, based on the information about twins, triplets and quadruplets?
• Others?

I may have missed the mark here. It is entirely possible that pregnancy is a topic to be avoided in Elementary school. So far, my daughter has played around on the math on this one for a day or two now without asking me any questions that I don’t want to answer.

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Ticket Roll Elementary Style

I get asked frequently if anyone is compiling 3-Act Math stories in the style of Dan Meyer or learning through problem solving activities specifically for elementary school. I’m not aware of anyone cataloguing them at the elementary level, probably because most elementary school teachers have to teach everything, not just math. It’s daunting, and probably hard to focus so much on one subject. Here’s the thing that occurred to me, though. Because Act I is typically completely visual, and we ask students what THEY wonder about, won’t they automatically wonder about things at their own level? I think that many of the ones presented on this blog would work in an elementary classroom with minor tweaks to Act II (and maybe Act III). I’ll use the ticket roll video I posted yesterday to explain.

Act I – Same Video Used for High School Students https://vimeo.com/69124531

I assume elementary school students will also wonder how far Sarah will get. The high school kids will get dimensions of a ticket and work with area and volume to determine how many tickets are on the roll. What if we just change the Act II information we provide for elementary school students?

Act II – Modified for Elementary School Tell the students that there are 2000 tickets on the roll, and show them the video below. https://vimeo.com/69173213

Act III – Same Video Used for High School Students Play the same answer video from my previous post. The answer is the same. The payoff is the same. The math is more elementary. https://vimeo.com/69123114 The answer the will come up with (by dividing) is actually a little too close. I was hoping it would be messier in the end so the students could discuss why it might not have been so accurate.

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Ticket Roll Reworked

The first time Dan Meyer came to Edmonton, he had us work on this problem. It was engaging, and a room full of teachers dug right in. The second time he came to Edmonton, he explained his 3-Act Math format. During that session, which was almost two years ago now, I came up with an idea for a video Act I and Act III for the ticket roll problem. My idea was to film a roll of tickets unravelling along a marked football field. The math remains the same.

I didn’t film it for a number of reasons. Marked football fields that don’t have Eskimos playing on them are scarce in Edmonton. It would require several cameras, and I had only one. It would require editing above my level of ability. This week, it all came together for me. We are doing more and more video editing in our work at AAC. We recently hired a NAIT student to do some of that work for us, and bought a shiny new computer and the Adobe suite. One of the student’s jobs was to teach us how to use some of that fancy equipment.

The way I learn technology is to immerse myself in a project, and seek support when I need it. Today, I did just that. I put together my vision of Acts I and III for this problem, with the NAIT student nearby for support. I learned a lot about video editing. It was a great day of learning for me. The videos are not perfect, but they’re better than I could have done last week at this time.

Enough Preamble. Here’s what I did. I give you Ticket Roll Reworked. Presented in 3 Acts, of course.

Ticket Roll Act I

Ticket Roll Act II

As near as I can tell, Canadian ticket rolls are identical to the American one Dan photographed. His Act II information should work out perfectly here. I have a different Act II filmed and not posted yet. I’m on it. I’m hoping it will take this problem to an elementary level.

Ticket Roll Act III

Sequels

Dan has sequels listed here.

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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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