Comments on: [3ACTS] Lucky Cow

By: Jared Cosulich

Jared Cosulich — Mon, 09 Jul 2012 21:29:55 +0000

Dan,

If you want to collaborate around building this type of application I would be happy to help. I’m working on a number of puzzle based educational apps that work similarly to what you are looking for:

http://puzzleschool.com/

Anyways let me know if you’re interested.

Best,
Jared

By: Steven Peters

Steven Peters — Thu, 05 Jul 2012 14:28:11 +0000

After reading a few of these comments, I realized a scenario in which the horizontal cut makes a lot more sense than the vertical cut from a practical perspective: when the slice is very thin (think cheesecake rather than pizza). In that case the length of the cut in the horizontal direction is much, much shorter than the length of a vertical cut. From my own experience, it can be tricky to make long straight cuts, so I would prefer the horizontal cut if it was much shorter than the vertical cut.

Regarding the whole matter of whether contrivance is a problem or not: I think you can still get mileage out of the problem, but I was distracted by the vertical cut issue, and I figured others might have been as well. It felt like it was almost there, so I was trying to help brainstorm a more natural scenario for the horizontal cut. In my opinion, I think it’s more practical when the slice is very thin.

By: Susan Russo

Susan Russo — Thu, 05 Jul 2012 00:20:06 +0000

I’ve Geogebra-ed the issue:

http://www.geogebratube.org/student/m13424

I wish I were a student again……………….

By: darren white

darren white — Wed, 04 Jul 2012 21:37:31 +0000

By Horizontal cut I meant, cutting it in the same way as the video cuts the beigal

By: darren white

darren white — Wed, 04 Jul 2012 21:27:08 +0000

This task has reminded me of an activity I set for a class of 15/16 year olds. I took in a round of Camembert Cheese. The task was to make 2 parallel cuts to slice the cheese into 3 equal parts.
They quickly rejected the Horizontal Cuts as trivial. They spent 100 minutes collaborating on the task then went home to finalise their solutions. the next lesson they presented their solutions and then took a vote on which was most convincing. Finally out came the chees knife. we weighed the results on scientific scales to see how accurate the solution was before eating the cheese. The solution was not very accurate for lots of reasons but the students were highly engaged, did an amazing amount of cognitive accelerating maths, had fun and ate cheese so all were happy

By: Fawn Nguyen

Fawn Nguyen — Tue, 03 Jul 2012 20:53:02 +0000

Then there are times when we WANT to learn more (and teach less) by saying, “Okay, a vertical cut is obvious, but obvious is easy. Let’s try to think about the horizontal cut…”

It would be contrived if a textbook made me do it, but if it’s put out as an invitation in the tone of “What do you think?” then I want to play the game.

By: Steve Phelps

Steve Phelps — Mon, 02 Jul 2012 16:14:19 +0000

I have an Nspire file that I used last year for exactly this kind of activity. Kids needed to graph the equation of a line that they thought would cut a given region in half. I will do my best to find it…

Now, I wonder how a GeoGebra file might look?

By: Simon Clough

Simon Clough — Mon, 02 Jul 2012 04:16:18 +0000

I like the task. I think that the second act could possibly be improved by simply showing the circular container with the remaining 7 wedges with its diameter (10cm). Hopefully the students could deduce that 8 even wedges would have an angle of 45 deg and a radius of 5 cm.

I think that some kind of interactive app/software that could be overlayed to analyse these images would be awesome. A ruler with an adjustable scale for a start, and why not a protractor. The collaborative aspect of comparing results certainly is a great idea.

Keep up the great work Dan, this is my first time post after lurking around for a while. Interesting to see where all this leads…

Cheers
Simon
Mullumbimby, Australia

By: Garrett Gray

Garrett Gray — Sun, 01 Jul 2012 04:53:12 +0000

Oh yeah, one more thing. A nice extension to send them home thinking about that might interest the still curious students is the following:

Insist that the cut starts at the point where the radius intersects the arc and extends in a straight line to the opposite side.

By: Garrett Gray

Garrett Gray — Sun, 01 Jul 2012 04:46:47 +0000

Very cool problem! I’ve enjoyed playing around with this, and I think my students will have a good experience with this. I’ve been teaching Math for 6 1/2 years in an English Program in Bangkok, Thailand, but I’ve just recently discovered this math teacher blog world.

Mr Bombastic brings up an interesting point on how things change if we use larger angles. I like how this leads to the question of how we find the cutoff angle and how we have to use a different method if the angle is bigger than x. Finding x is also interesting as it reduces to an innocent looking x = sin(x/2) and the possibility of using graphical intersections to solve an equation.

Thanks for providing so many interesting ideas in this blog, Dan!