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Posts Tagged ‘Math 10-3’

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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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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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

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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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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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.
  • 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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Thanks to this post on Dan Meyer’s blog, and an ensuing conversation between Dan and Curmudgeon, I was pointed to an article that I think would make a pretty compelling problem in Math 10C or Math 10-3 measurement.

The article describes a 17 year old driver who was given a $190 ticket for going 62 miles an hour in a 45 mile an hour zone. His parents, however, had installed a GPS system in his car to track his speed and driving habits, and they claim the GPS proves their son was only going 45 miles an hour at the time the ticket was issued. It appears to have taken two years of legal wrangling, before the ticket was finally upheld, and he had to pay the fine.  I wouldn’t tell the students that yet, though.

Here’s a link to the article: Speeding Teenager

Lesson Plan

1.  Present the problem.

Give the students the following excerpt from the article:

Shaun Malone was 17 when a Petaluma police officer pulled him over on Lakeville Highway the morning of July 4, 2007, and wrote him a ticket for going 62 mph in a 45-mph zone.

Malone, now 19, was ordered to pay a $190 fine, but his parents appealed the decision, saying data from a GPS system they installed in his car to monitor his driving proved he was not speeding.

What ensued was the longest court battle over a speeding ticket in county history.

In her five-page ruling, Commissioner Carla Bonilla noted the accuracy of the GPS system was not challenged by either side in the dispute, but rather they had different interpretations of the data.

All GPS systems in vehicles calculate speed and location, but the tracking device Malone’s parents installed in his 2000 Toyota Celica GTS downloaded the information to their computer. The system sent out a data signal every 30 seconds that reported the car’s speed, location and direction. If Malone ever hit 70 mph, his parents received an e-mail alert.

Malone was on his way to Infineon Raceway when Officer Steve Johnson said he clocked Malone’s car going 62 mph about 400 feet west of South McDowell Boulevard.

The teen’s GPS, however, pegged the car at 45 mph in virtually the same location.

At issue was the distance from the stoplight at Freitas Road — site of the first GPS “ping” that showed Malone stopped — to the second ping 30 seconds later, when he was going 45 mph. Bonilla said the distance between those two points was 1,980 feet.

2.  Ask the students to discuss the article.  In the end they will come to the question we want explored.  Was young Shaun guilty of speeding?

3.  Let them answer the question.  Have them prepare a defense for Shaun, or an argument for the prosecution.

4.  Show them the Commissioner’s conclusion, based on mathematics.

Bonilla said the distance between those two points was 1,980 feet, and the GPS data confirmed the prosecution’s contention that Malone had to have exceeded the speed limit.

“The mathematics confirm this,” she wrote.

Teacher Resource

A possible solution

An extension, eventually.

I have been attempting to contact the person mentioned in this local article, but so far he hasn’t responded to me.  Similar mathematics could prove he wasn’t driving as excessively fast as the red light camera claimed, but I would need to get a copy of his ticket to show that.

Red Light Camera

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October’s issue of the NCTM Mathematics Teacher magazine included an excerpt from an interesting article in their Media Clips section.  They used a Forbes article that dealt with tween earnings, and the portion they included is:

Hollywood’s 10 top-earning tweens collectively pulled down $107 million between June 1, 2007 and June 1, 2008.   According to Alloy Media and Marketing, it’s a rabid and often indulgent fan base: America’s 20 million kids aged 8 to 12 spend $51 billion of their own money annually and influence $150 billion more in spending by their doting parents. Tied for the top spot: Hannah Montana star Miley Cyrus and Harry Potter lead Daniel Radcliffe. The young talents each banked a cool $25 million in the last year.

I love this article for the questions it could elicit.  The problem with the Mathematics Teacher Magazine treatment of this is that it follows the article with 8 questions we are supposed to ask kids.  Teachers might see this, and defer to the questions provided, thereby missing a great opportunity.  I’d much rather show students the article, and have the kids decide what would be interesting to explore further.  There are lots of potential rate and ratio questions that could come from student exploration here.

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