So, I am kind of on a binge right now with my 3 act posts, but I have had this one for awhile and I have not posted it, but after reading this comment on Dan Meyer's blog I decided I should put this up as a possible elementary level 3 acts lesson.  Here it is....

I have a goofy little set up for this, where I say I'm making drinks for my friends, do I have enough?

Ask them what they think?  If so how many glasses do you think I can fill?  Give me a number that is too high and a number that too is small.  Ask your students what information we need to know.  Then we are on to Act 2 (and here is where the differentiation comes in...

If you want students to find the volume of each of these containers you can use these pictures to do the trick (jump-high-five for differentiation!).

When it comes to anyqs, I find that the ones that interest me the most are the images or videos that blow my mind by sheer scale.  A seven wonders of the world sort of deal rings deep within my soul, and so I offer you MEGACOIN!  

HOLY CRAP THAT IS HUGE! Here is where I would ask "How much is this coin worth?" Let students ask questions.  I am debating if I want to let them know it is made of pure Gold or should I let them follow any rabbit trail they want.  They'll probably guess it's gold.

There is a lot that goes on with this one.  We have volume, density, rates, ratios, it is all fantastic!

And the final answer is...

I have actually been able to think of a few cool sequels based on this (which makes me happy since this is the hardest part for me).

• What could the dimensions for a true million dollar coin be? A billion dollar coin?  A trillion dollar coin?
• Using the following chart, how much would this coin be worth today?  Did the people that bought these make a good investment?

I have a penchant for dinosaurs and monsters that roamed the Earth millions of years ago.  I still remember sitting in the theatre when I was six years old to see Jurassic Park.  I remember the first moment that I saw the Brachiosaurus in that movie and ever since I was hooked!  I have never grown out of that.  Watching Jurassic Park still makes me giggle like a school girl. When I see things like quake circles in glasses of water, and the piercing cry of the velociraptors, my heart soars!.  Suffice to say when I first learned of something called the Megalodon I was hooked.  Here are my 3 acts.

Megalodon was a shark: a really really big shark.  What is different about finding remains of a shark than say that of a Tyrannosaurus is that a shark is mostly cartilage.  That means that scientists mostly only get to find jaws and teeth.

So I want to ask students: "If you found a tooth this size, how big would the shark be?"  *Side note for extra awesome go buy a replica on ebay!* Get guesses, draw pictures! Give them a grid to show scale between you and the size of the shark, all in the name of awesome!

Now experts recognized that this is a shark tooth by comparing it with one of the fiercest sharks around.  The Great White shark actually shares much the same characteristics as the Megalodon.  Hopefully students will recognize that if we have identified it as a shark tooth that we can compare it to these sharks.  This is where some comparison pictures come into play.

Students now can make some educated guesses, and we can talk about what are some good methods for estimating Megalodon's size.

The first estimations were done very simple proportional reasoning, which gives us the overestimate. At this point I might have students measure out on a string how big the Megalodon actually is!

There are a few sequels that come to mind.

• Given a length of a shark, draw the size of its tooth.
• Experts thought that assuming a directly proportional relation was not accurate measurement.  Some experts (Gottfried et al.) found the following information to create a formula that predicts the size of a shark.  Use the information in this table to find the equation, and use it to make a new estimation of our Megalodon's size. 

Well tell me what you think!  I am so excited about this, but will it translate?  What do ya think?

Listening to Dan's talk on iTunes has makes me really want to post this, because this is the one problem that actually caught my curiosity.  I was driving home one day, noticing these nice dotted lines on the highway as I came home.  I wondered what I could do with it, and so I made my carpool friend drive home one day...

I especially like this, because I feel like it is the "wizardry" of mathematics, something so innocent, could tell someone so much.

Some other very vital information is what is the distance.  Well if you are from the US of A (do americans actually say that?), you can use this great article, just keep in mind my video is shot in Canada (so Km/h), or as my Blair Miller helped me find you can use this resource for British Columbia...

Or just pull out Google Earth and measure, that mother is pretty precise.

And there it is.  I feel as if I may have cheated you guys out of the reveal, just doing the picture in picture.  Would have been better show me pull in the camera onto the dashboard?   What do you think?

Where I could see this going is A) develop the general case for m/s to Km/h.  Or better yet lines/sec to km/h (MPH if you are a friend of Uncle Sam (do Americans ever say that?  I need to get cultured)).  For some reason I feel like this would be a sweet app, have students make it.  I also thought of bringing in movies, car chases, to see how fast they are really going.  This one even mentions some of the speeds in the intense Bullitt car chase.

How else could I extend this?  I don't know, but I think my grades should have fun with it...