Category: Volume

3 Acts - Mmm Juice

1/5/2012

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....

Act 1 - Mmm Juice....

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...

Act 2 - Measurements (Grades 4-6?)

Act 2 Measurements (Grades 8-10)

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!).

Act 3 The Reveal

Sequels

How many cans of juice do I need to give one cup of juice to the whole class? To the whole school?
How big of a container do I need to hold all the juice for the whole class? The whole school?

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3 Acts - Mega Coin

1/5/2012

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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!

Act 1 - The Coin

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.

Act 2 - The measurements

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

Act 3 - The Reveal

And the final answer is...

The Sequels

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?

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3 Acts - Viva Las Colas!

11/19/2011

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So apparently I really like pop as you can see here and here. Before we begin I feel I have to let you know my teeth are not rotting, and I do not have a coke addiction, okay clear? So here's what you came for

Act 1 - The Really Big Bottle!

This is the Coca Cola store in Las Vegas Nevada, and when we went in for a drink, we were pleased to read the trivia on our drink tray. This is what we found.

Score!

Act 2 - Measurements

The trivia tray also had some vital information for our cause, here it is. I was trying to figure out the best way to edit these images. I would like to here some critique of my design, to try to find out what looks best, but this is my attempt.

The way I saw solving this was to map some function to the coke bottle, and use our lovely calculus to find the volume by rotating, so I developed a bare bones Geogebra app with sliders and the picture to find a sinusoidal function that would work (an assumption I made, too much for students?). I wonder if this should be an Act 2 artifact or if students should come up with this themselves.

coke.ggb
File Size:	1526 kb
File Type:	ggb

Download File

Act 3 - Reveal

As I am sure you have seen these sorts of answer reveals on trivia trays, they have the answer flipped upside down, and once again, I am not sure of the best way to present this reveal. So here are my two copies of the reveal.

Possible Solutions

As I already stated I used rotation to find the volume, then I had to convert to ounces, and then divide by 8. With GGB I found these equations and these points.

And I allowed wolfram to do the rest

solution_-_coca_cola.pdf
File Size:	244 kb
File Type:	pdf

Download File

In wolfram it converts it to "ounces" but the final answer is really number of 8 ounce coke bottles, and with a number greater than 6 million, I think I can say that we need to have a talk with the math coordinator at Coca Cola Las Vegas. (Assuming I used my math right, could you guys check that for me?)

Sequels

I can think of only a few...

Create a scale picture on GGB (using either a cylinder, or a sphere from the front, or a bottle) to show the true size of 8,000,000 ounces.
If we could fill this coke bottle with 8,000,000 ounces, how full would the bottle be? Did the "math coordinator" account for coke bottles having air?
How much would it cost to fill a coke bottle this large? How much would it cost a consumer to buy that much Coca-Cola?

And without further ado the complete package zip file.

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3 Acts - Mmm Juice

Act 1 - Mmm Juice....

Act 2 - Measurements (Grades 4-6?)

Act 2 Measurements (Grades 8-10)

Act 3 The Reveal

Sequels

3 Acts - Mega Coin

Act 1 - The Coin

Act 2 - The measurements

Act 3 - The Reveal

The Sequels

3 Acts - Viva Las Colas!

Act 1 - The Really Big Bottle!

Act 2 - Measurements

Act 3 - Reveal

Possible Solutions

Sequels

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