Geogebra Doodads

Geogebra is a great tool for communicating mathematics.  In recent versions, developers have added the ability to export to HTML5 (as opposed to Java) making it even easier to share a ggb file.  In addition, an animated .gif file can be created from any ggb file with a slider in it.

In the past, I have dumped my various student activities and teacher presentations in one large directory.    Now, I want to start putting out my work in a little more organized fashion, by introducing them on the blog and tagging and labeling.  For now, I’ve decided to call them “Doodads”.  Perhaps a better vocab word is out there to represent the interactive, mathematical, and curiosity sparking nature of these creations.

Here is the first one:

Time Angles (ggb doodad)

In the spirit of Dan Meyer’s WCYDWT, what is the first question that comes into your head?

The “answer” :

Copper Tiling… classic WCYDWT

Ran across this on reddit

The smile inducing “how much does it cost?” is a great place to start.

But how about “how much area is wasted?” to touch on the packing problem of circles. http://en.wikipedia.org/wiki/Circle_packing_in_a_square

And hey, might as well kick it up into 3D… http://www.youtube.com/watch?v=uDJ3sor2oQ0

WCYDWT / 101qs: 13 Folds

Dan Meyer has morphed his “What can you do with this” edu-meme into “#101qs”:  what questions pop into your head upon observing a picture, movie, or other demonstration.  The more likely it is that a student will ask that question, the better.

I will present one now.  For your consideration,

“13 Folds”

13 Folds

If you tossed that up in your class, what would the kids say?  What’s the first question that pops into your head?

I’ll offer my own thoughts, and I welcome you to share yours in the comments.

I think this image has a lot of things going for it.  It is clearly the ACT1 image.  Toss it up.  Don’t say anything.  What will the kids ask?

What is it?
Toilet Paper.
That’s hella toilet paper!  (excuse the norcal slang 😉 )
yeah!  it’s a lot!
How much?
I dunno.
What do you mean you don’t know!? you’re the teacher!
Can we figure it out?

At this point, you can go to ACT2:  Have the students figure out what they need.  In this case, there’s a rather nice ACT2 image:

Act 2

Alternatively, you could say 5 feet by 2.5 feet on the image.  Or if you’re really brave, you could estimate it by the heights of the kids in the screenshot.  Ideally, you don’t have to say much else.  To a stuck student I might offer only: “unfold it“.

Extensions:

  1. Graph it.
  2. How many rolls did they buy?  What did it cost them?
  3. How thick is the paper?  Graph THAT.
  4. How many layers are at the 13th fold?  Another graph to make!
  5. Why toilet paper?
  6. What is preventing the 14th fold?  Why did they stop?

And finally,

Act 3

Ah, but there’s a bonus:  we have the actual video of them doing the folds.  What a great way to end the class!

http://www.youtube.com/watch?v=vPFnIotfkXo

Why toilet paper?  Try the Mythbusters episode: http://www.youtube.com/watch?v=kRAEBbotuIE

And then for those super interested kids who can access the final extension questions, you can lead them through Brittany Gallivan’s solution for arbitrary paper: http://en.wikipedia.org/wiki/Britney_Gallivan

Credit to Dr. James Tanton http://www.jamestanton.com/ for leading the actual exercise at MIT.

Toss me some comments!

WCYDWT: Displaced Water

In brainstorming about opposites and the additive inverse, I came up with an idea about justifying one step equations with this displaced water video.  But, it doesn’t quite lend itself to subtracting from both sides.  I’m going to try this as is, and perhaps we can come up with ideas in class about how well this lends itself to x+800=____ish.

I think this could also take a geometry route.  It reminds me of the demonstrations that a cylinder of height 2h and radius h has equal volume to (a sphere of radius h + a cone of height and radius h).

But right now, the ideas are in their infancy.

P.S. what did you get?  Here is the answer.

WCYDWT: Escalator

In the style of Dan Meyer’s WCYDWT… I may not have time to do a full lesson around this in my Algebra class.  There are only 4 days left and we are rushing through  the required tests.  But inspiration hit me when I saw this view:

I

Click for video

I put it up in my small 6th period class to get a taste for  how things would go.  Students immediately related to it (one kid correctly named the BART station) With a little prodding — “did you see the guy with the bike who was bookin’ it?” — they talked about how fast people were going.  Then they talked about trying to go down an escalator going up or up and escalator going down.  We didn’t get to any sort of problem solving, but we did count that it took about 30 seconds to merely ride the escalator up.

More on this as it develops… especially if I have time to implement it fully.