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3 Acts - T.V. Space

1/12/2012

9 Comments

 
I am learning more and more about how this whole problem based learning shtick works, and I have to say I love it.  Today was an example of how much I love it, and how worthwhile it is.  I have been struggling to motivate the use of the Pythagorean Theorem in a natural way so that students can jump in.  Enter Mr. Piccini's Summer Purchase...

Act 1 - My Living Room

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I started off the "story telling," by discussing how it was time for my wife and I to upgrade our T.V. I showed them the picture and asked them: "What problems do you think I may run into?"  I realised after that this was a little too much of the "Guess what is in the teacher's head" but the question was so natural they needed to ask "Will the TV fit under the shelf?"  We talked about what it meant for a TV to be 40".  Almost half the class knew that it meant the diagonal.  I asked what do we notice about the shape of a TV is when cut down the diagonal.  Clearly there were two triangles, and thus began our exploration.

Act 2 - Exploring the Pythagorean Theorem

For the next part I stole the great investigation from Dan Meyer found here.  This worked so well it was unbelievable. Students were very quick to see the relationship between the sum of the small areas and the large area.  Students enjoyed the manipulative nature of this exploration, and the result was clear and accessible to the students.

We did some practice and then came back to my T.V. the next day.

We started the next day with whiteboards, and I had students write what information we knew and what information we needed to know.  I reinforced to students that I did not want to renovate my wall because I am lazy, but I am not too lazy to move my speakers.  They said then that we needed to know the height to the shelf. So I gave them this...
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Depending on how hard you want to make this problem you can do either cm or inches.  Inches is the easiest.  Since students recognized that we need information on the diagonals, we need to talk about what a good diagonal measurement would look like for this space.  For that I broke out geogebra, to show students how sizing TV's looks.  I used these two geogebra apps.
non_scaled_tv.ggb
File Size: 23 kb
File Type: ggb
Download File

scaled_tv.ggb
File Size: 22 kb
File Type: ggb
Download File

We talked about what the different shapes of TVs look like, and what your average wide screen would look like.  Using the geogebra animations the students discussed how the proportions always stay the same.  At which point we could talk about ratios.
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At this point students needed guidance on how to find the dimensions of the space, but it came quite naturally to talk about the largest possible TV that I could fit in my living room.  Students found that this was a 55" TV, and as it turns out...

Act 3 - The Reveal

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Sequels (Updated May 27, 2012)

If you don't believe in collaborating online via blogging etc. let this section be a testament to this.  Neither of these extensions were my own thoughts, they were completely lifted from others, awesome!
  • Megan-Heyes golding submitted this awesome picture on 101qs.com.  I am sure that any of the questions there will do, but the simplest is: "Is that true?"
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  • From Karim in the comments there is also this: "What is the largest standard TV (4:3) that could fit in this space?
Online collaboration for the win!


Reflections

This was such a simple execution, but it gave the students a real challenge, and a real-world application to try from the get-go.  I had a debrief with my students in one class, and they said they loved how visual, real, and engaging it was.  I never expected to hear that.  The only complaint was from students that finished really quickly.  I was not ready with sequels, and in fact, I still can't think of any. I never thought that this specific problem would have as much engagement as it did, but once students got rolling they were hooked. All in all I was happy today, and I sure beat the socks off this version of the problem.
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9 Comments
Damian Watson
1/12/2012 03:24:33 pm

Brilliant! Real life example to the extreme, I particulary like the laziness comment about moving the speakers. Great three act! Thanks another lesson to use!

Reply
Timon Piccini link
1/12/2012 03:41:22 pm

Thanks for the support Damian! I hope it works well in your class.

Reply
Karim link
1/17/2012 05:20:33 am

Great stuff. For extensions, you could ask them the largest standard TV (4:3) that would fit. You might also extend it to other devices like the iPad, where you don't necessarily know the aspect ratio but rather the pixel dimensions.

Reply
Timon Piccini link
1/18/2012 02:57:56 pm

Thanks Karim! Those are great. I will definitely use them next year.

Reply
Rob
3/9/2012 05:15:17 am

That's one of my favourite questions in that textbook. Lots of good discussion. "Why would the company give the height and width in an advertisement when they're lying about the size of it?" Or if the consumer is doing the measurements: "Why didn't they just measure the diagonal?"

Reply
Michael P link
5/8/2012 12:04:02 am

Any advice for me? I tried the investigation for the Pythagorean Theorem, but ran into some trouble. The kids had trouble getting exact answers with the pieces. The difference between an acute triangle and a right triangle was often a matter of opinion or judgement.

Reply
Timon Piccini link
5/8/2012 02:36:43 am

I got students to put a star or question mark besides any contested measurements. If they can't agree, put a star beside it.

Then find the pattern of the ones that are clearly obtuse or clearly acute. The start to develop the inequality. If the sums are less than than the square of the longest side, we have an obtuse triangle. If the sums are greater than than the longest side we have an acute triangle.

Then I ask what happens if the sums are exactly the same? They usually come up with 90 degrees.

Then we look at the contested, do some of them come REALLY close to equal without being equal? Yes, that means the angle is probably 91 degrees or 89 degrees. Then ask them where those errors of measurement come from.

Clear?

Reply
Michael P link
5/8/2012 04:40:46 am

Oh dear...you're good.

It's this sort of attention that I'm always messing up in the classroom. Thank you so much. I need to figure out how to get better at this.

timon.piccini@gmail.com link
5/8/2012 07:00:05 am

This was learned through much trial and error.

Reply



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