Perimeter+of+a+triangle

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If the lengths of all three sides of a triangle are integers, and the length of one side is 7, what is the least possible perimeter of the triangle?

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 * Solution by Tim Fahlberg**:
 * This is a somewhat interesting problem having to do with the Triangle Inequality (the sum of any two sides of a triangle has to be greater than the 3rd side).
 * Here's my [|solution]. I'm not entirely satisfied with it but I think it's likely correct unless I missed something I should have seen. Can anyone do any better? -- Tim Fahlberg

I have created a [|hands-on activity] that might help. I am approaching it the same way you did Tim but with a manipulative. I could make a movie an elaborate but I'm hoping that won't be necessary, especially combined with your explaination.
 * Offer by Robert Fant**

I had a go with your virtual manipulative (created with a free Java applet that reminds me of The Geometer's SketchPad and loved what you had done! Here's a [|screencast/mathcast] * of my work. After I made this movie I realized that I hadn't shown a triangle with sides 7, 1, and something else so I'd like to invite anyone reading this to experiment with Robert Fant's wonderful virtual manipulative and see if you can make a triangle with sides 7, 1, and some integer and make a triangle that beats our record (I don't want to say what it is because the whole point of mathcasts and collaborating this way isn't just to get a final answer - it's the process and the sharing of thinking and reasoning and the collaboration between us that's most important).
 * "Wow!" Says Tim Fahlberg**

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 * 4 important notes about this screencast/mathcast:
 * 1) It was created with Camtasia Studio 4 and uploaded to Screencast.com.
 * 1) I used the ScreenDraw feature in Camtasia Recorder for the first time to do the highlighting. ScreenDraw has a bunch of other features in it like arrows, a drawing pen, etc.
 * 2) I produced the screencast using a Production Preset of Screen Recording to Web.
 * 3) I had never used this Java Applet before so I did play with it for about 5 minutes before making the movie.

BTW: Robert Fant and I (Tim Fahlberg) have never met in person. In fact, Robert and I only met through the internet a few days ago when he shared that he and his students were making mathcasts. I invited Robert and his students to look at this collaborative wiki and pose or answer questions. **I consider this solution to be a great example of what's possible with asynchrnonous collaboration facilitated with mathcasts. What do you think?

+++++++++++++++++ Tim, Thank you for so many kind words. It is a pleasure working with folks that share the same passions. Hey, ya gotta love the internet. It is the tool that allows such things to happen.** After watching your mathcast, and on my wife's advice, I went in and added a coordinate system and have points "snapping to" integers (somewhat), making it a little simpler to "see" (and control) what is happening with the lengths of the triangle legs.

[|**View it here.**]

Side Note: The applet I am using is an "open-source" project and can be freely downloaded from http://geonext.uni-bayreuth.de/ It is very similar to Geometer's SketchPad but it's Java capabilities are FAR superior to SketchPad's. The unfortunate thing about it is that its documentation is all written in German (not translated as of yet.)


 * Feedback from cmk7**

What I liked about Tim's mathcast was that the solution wasn't worked out in advance. It is important for students to experience how mathematicians think through the problems that are presented to them. Actually, it's important for less experienced math teachers to watch that process as well. Mathcasts could play a significant role in teacher training. Pre-service teachers could create mathcasts as a way of improving their art and could watch the mathcasts of veteran teachers for examples of best practices.

In the near future, the math problems will require more specific categorization.

I was unable to use the manipulative. I'm using IE 6.0 and can usually interact with applets. The program loaded to some extent but I could not see the interface that Tim had in his mathcast. Based on the mathcast, the program added a lot to the explanation. We might want to consider incorporating tools like that whenever possible.

Thanks for the postive feedback. Dr. Robin Kay (math education professor in Canada) has been working in the area of having his preservice teachers create mathcasts. Here's a link to their work: http://education.uoit.ca/EN/main/151820/151827/research_teach_emc.php. I introduced Robin to mathcasts several years ago and sent him a wired SchoolPad back when I was selling totally enamored with them. His students do some excellent work and I think will find it much easier to get their first teaching jobs when they show their portfolio (or have it open doors for them before they even get to interviews).
 * Feedback from Tim Fahlberg**

I agree that we'll soon need to develop better categorization for problems. We're also going to have to determine if we should have two separate sites - one for students to ask questions of others and one for teacher desiring professional development. What do you think?