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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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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Book Sale

I’ve been using this video for over a year now in presentations on the revised program of studies. My intention in showing it is to demonstrate a problem with number sense in our society in general.

I have spent a year making fun of the Verizon people’s mathematical abilities. Today, however, I am ashamed (and a little amused) to admit that someone in the employ of the same district I work for has made the exact same error. An astute EPSB math teacher sent this flyer my way today.

Show your students this flyer. Ask them what they wonder about.

I would have them calculate how much 100 pounds of books will cost. See if they make the same faulty assumption that I believe the person creating this flyer must have made. I can’t believe they really intend to sell the books for half a cent per pound. If that is true, I’m rushing right over on Friday to get my 100 pounds of books for 47 and a half cents.  I’ll even give them 48 cents and let them keep the change.

Give your students extensions. How many pounds of books could they get for $20 at this rate? Would all those books fit in a car? What about for $100?

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China Wedge – Three Acts

While in the Pennsylvania Convention Center for ISTE 2011, I came across this intriguing piece of art wedged under an escalator.

I have since learned that the piece of art is by Mei-Ling Hom, and is called “China Wedge”. It  is composed of many Chinese cups, bowls and spoons wedged into a space under an escalator. It appears that the space is not entirely filled with cups, bowls and spoons, but they go about 2.5 deep all around. The sculpture, which was commissioned for the Center’s Arch Street Concourse, pays homage to Philadelphia Chinatown, which is adjacent to the Convention Center. (Source (Spoiler Alert):  http://philadelphia.about.com/cs/artmuseums/a/paconvention.htm)

I took some photos, because I wanted to turn this into a math story. I didn’t get all the shots I needed, so I have to give a big thank-you to Max Ray, who went back and took care of the Act II photos with his girlfriend, who happens to be a photographer and got great shots. The Act II photos containing referents and shots of Max are all the work of Kaytee.

Here is my attempt at a three act math story as described by Dan Meyer here.

Act I – The Video

Act II – Some More Information in Photos

• The Escalator
• Close Up of China
• Close Up of China With Referent
• Wide Shot of China Wedge
• Wide Shot of China Wedge With Referent (Vertical)
• Max’s Height
• Wide Shot of China Wedge with Referent (Horizontal 1)
• Wide Shot of China Wedge with Referent (Horizontal 2)

Act III – The Answer

• Word document containing all the information I could find about the China Wedge.

Sequels

I struggle with this one.  Any feedback would be greatly appreciated. I’ve only one idea so far.

• If the entire area under the escalator was filled with cups, bowls and spoons, how many more would have been needed?

In his last one of these, Dan asked whether this broad outline is enough for teachers to go by. I know it is enough for lots of us to run with. If you need more details about how to make this work in a classroom, contact me and I will spell it out a bit more. I would present it in much the same way I discuss in my learning through problem solving explanation.

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Can I Make it to Calgary?

This one didn’t get much love when I threw it out on Twitter under the #anyqs hashtag.  I still think it has nice use in a Math 10C or 10-3 class on measurement.

It’s a bit of a shaky video, so I paused it at the crucial parts.  If it’s still hard to tell, I’m sitting on the side of the road.  I have about a half tank of gas.  My truck tells me I can go 163 miles until empty.  The sign I’m stopped at tells me it’s 16 km to Leduc, 137 km to Red Deer, and 275 km to Calgary.

Let’s fit this into the 7 steps of LTPS.

1. Play the video. 
2. Ask the students what they wonder.  They will likely wonder where I can get to before running out of gas.  I was wondering if I could make Calgary.
3. Ask them to guess how far I can get.  Near Calgary?  Past Calgary?
4. Ask them what other information they require to solve the problem.  They will likely need some conversion factors.
5. Students solve.  Teacher circulates and offers support and/or extensions.  Extensions could involve litres per 100 km or miles per gallon based on the fact that I have a 100 gallon tank in that truck.
6. Students share answers. The teacher can’t play an answer video, because I didn’t actually drive until I ran out of gas.  Sorry I didn’t take that one for the team for the sake of math education.
7. Teacher summarizes learning with a brief wrap up on metric to imperial conversions.

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The Sandbox

Since I was filling my daughter’s sandbox anyhow, I decided to film it and turn it into a math problem.  I’ll fit this into the 7 steps of the Learning Through Problem Solving approach discussed previously on this blog.  Here’s how to make this work in your classroom.

• Play the question video.

• Ask students what question they want to explore.  They will likely come up with “Does he have enough bags of sand?” or “How many bags of sand is he going to need?”
• Elicit student guesses.  Students may assume the answer is 20, because that’s how many bags are stacked up.  You should tell them that the guy in the video is a notoriously bad measurer, and he could have way too many or way too few. As a class, agree on a range of reasonable answers.
•  Ask the students what further information they need to answer their question.  Provide them the measurements of the sandbox, and the information from the bag of Play Sand as shown on this handout.

View this document on Scribd

• Allow students to work on the problem.  Students who finish could be given an extension like this Google image of a local playground.  Tell them that the sand was put in at a uniform depth of 15 inches.  Ask them how many bags that would take. I would use a park near their school that they might remember playing in as a child.

• Share student solutions.  Have students share solutions with other students, or with the whole class using a document camera or chart paper.
• Play the answer video.  Discuss sources of error.

• Summarize what was learned about volume.

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The Giant Gummy Bear

@dandersod posted the following video on his blog last week.

He asked, of course, What Can You Do With This?

I decided that there was a lot I could do with it, so I worked on some editing of the video, and then I rolled it out with a group of teachers this morning to see where it would go.

Before I describe the lesson, I should point out that my first edit of the video involved crossing out some of the measurements the original video contained, as well as beeping out the commentary that mentioned the measurements.  I was limited by my video editing skill, and the software I was using. It ended up being awkward and kind of annoying, so I re-did it simply by deleting the parts I had originally wanted obscured.  The new video was much cleaner, and it had the extra benefit of not being so obvious about what I wanted students to explore.  With the beeps and blocked out numbers visible in the first edit, it was painfully evident what I wanted people to find.  The second edit allows for many more directions to be taken in the exploration, and it’s not even obvious that I have deleted anything.

Here was my lesson plan.

1. Provide each group a ruler and a 60 g bag of gummy bears.
2. Play the question video.
3. Ask the students what they wonder about after seeing the video.  In this edit, they will wonder about a whole bunch of things.  I’m hoping they get to, “How many small gummy bears are equivalent to the giant bear, and what are the  dimensions of the giant gummy bear?”
4. Elicit guesses, lower bounds, and upper bounds of reasonable answers.
5. Ask them if they need any clarification or information that might help
6. Turn them loose.
7. Work the room.  Help those who are struggling.  Provide extensions for those who hammered through it.
8. Have students share their answers.  They will be all over the place here.  Those that work with the calorie count will be closest to the “right answer”.  Those that worked with the mass will be a bit farther out.
9. Play the answer video.
10. Discuss discrepancies.  Is it measurement error?  Problems with the calculations?  False advertising?
11. Eat the gummy bears.

The lesson is fun, engaging, and has great curricular fit to Alberta’s Math 20-2 course in the measurement and proportional reasoning units.

At step #3 above, some members of the group I was working with really wanted to go a different direction.  Their suggestions became cool extensions for those that got done quickly.

1. How tall is the man in the video, who is the same height as the gummy bear from 30 feet away?
2. How many times would you have to walk around the school to burn off the giant gummy bear?

Enjoy

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