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Archive for the ‘Problem Solving’ Category

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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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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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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After attending a session on our revised curriculum by Dr. Peter Liljedahl, several teachers have told me that they have been inspired to spend the first week of Math 10 Combined on  establishing collaborative and problem solving practices in their classrooms.  Since we will be teaching math in a different manner than teachers and students are used to, it is important to create a safe environment in which students can explore and construct meaning through rich problems.

The idea that we will spend the first week on processes and exploration, rather than on checking off the first few curricular outcomes is frightening to some teachers.  Several have asked me what types of problems they should give students during that first week.  Below are three of my favorites.  They have loose curricular fit, but all allow for rich discussion, debate, exploration and invite multiple methods of solution.  The idea is to throw these out to students before any teaching has happened, and allow them to use any method they can to solve them.  Feel free to give me feedback, and share your own favorite problems.

Problem 1 Fred’s aunt is twice as old as Fred was when she was as old as Fred is now.  How old is Fred and how old is his aunt?

Problem 2 Three businessmen check into a hotel (in the olden days, when hotels were cheaper).  The desk clerk charged them $30, so they each paid $10.  Later on, the desk clerk realized he had made a mistake, and the room charge should only have been $25.  The desk clerk sent a bellboy up to the room with $5 change.  Unsure how to divide the $5 evenly among the three men, the bellboy gave each man $1 back, and kept $2 for himself.  Now each man has paid $9, for a total of $27.  The bellboy has $2 which brings the total money up to $29.  But the men originally paid $30.  Where is the missing dollar?

Problem 3 – The Jail Cell Problem In a prison, there are 100 cells numbered 1 to 100.  On day 1, a guard turns the key in all 100, unlocking them.  On day 2, the guard turns the key in all the even-numbered cells, thereby locking them.  On day 3, the guard turns the key in all the cells numbered with multiples of 3, thereby altering their state.  For example, if the cell was unlocked, he locks it.  If it was locked, he unlocks it.  On day 4, he turns the key in all the cells that are numbered with multiples of 4, thereby changing their state.  He continues this process for 100 days, at which time all the prisoners in unlocked cells are set free.  Which prisoners are set free?

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