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Posts Tagged ‘Math 20-3’

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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Roller Coaster

I got this idea from Frank Sobierajski at the ISTE 2011 conference.  It fits nicely in our Math 10C and Math 20-3 curricula. His take on the subject is available on this teacher tube video.

I took his idea and found a Canadian roller coaster.  Let’s take our students on a virtual roller coaster ride.  Most roller coasters have Point of View (POV) videos available.  I suggest finding one near you.

Bring up some facts about the roller coaster.  This one claims to have a 75 degree drop.

Find a picture of it, like this one.

Source: http://en.wikipedia.org/wiki/File:900behe.jpg

Have students import that image into GeoGebra, and check the math behind the 75 degree claim.

This 75 degree claim is either false, or the angle on the picture I found isn’t right. It’s possible that I haven’t measured from the same places they did. No matter what, it’s a good conversation in class.

I would follow up by having students find their own and check the claims made about them.

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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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