Popping Popcorn in a Popcorn Popper

Popcorn Question from David Cox on Vimeo.

Most of my previous attempts with these story problems have resulted in me slapping on a timecode and cutting the video.  This one had me thinking a bit.  I'm not sure I got it.

Your assignment:

1.  What question does this provoke?

2.  If you have a tough time answering #1, what question do you think I was after?  And what can I do to help that question along?

Act 2's a Killer

I need a little help.  I think I've nailed the question:


Barbecue Q2 from David Cox on Vimeo.

But I can't figure out what to give students to help them through Act 2.

Here's the raw footage and the current conversation and Greg's run at the data.  (Thanks to @maxmathforum for archiving)

Any help would be appreciated.

Download Time

I kept reading about all the fun everyone was having with the ProjectEuler thing, so I thought I'd give it a try. I thought it was pretty easy until I got to that one problem where they ask you to add up all the multiples of 3 or 5 that are less than 1000. I hear that people are using Python and letting the computer do the number crunching.

So, I think to myself, "Self, you took Pascal about 20 years ago back when RAM was measured in single digits and you said 'bless you' if someone said, 'gigahertz.' in college and absolutely hated that freaking class came out a better person because of it. This may be something you don't have time for, I mean you have 5 kids. Wake the heck up an enriching experience. And besides...Pascal...Python, they both start with Ps yeah, that's probably the only thing they have in common. You got this, man. G'head, give it a try."

I go to the Python site and read every thing I can to figure out which version would best suit me. (There's a lot to choose from, you know.) I can't find anything anywhere. It's all so confusing. Please. Someone. Give me a nudge in the right direction.

So I take a shot in the dark and go with v.2.7.

Anyway, this isn't really about Python. It's about the video I grabbed while downloading the program. I'm going to have my kids wrestle with it after break.

Download Time (Question) from David Cox on Vimeo.

I may not ever find the solution to that really difficult problem about multiples of 3 and 5, but at least I got a lesson out of it.

Build Your Own

What can you build with this?


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


Download GGB File

Which One's Best?

Two questions:

1.  Is the question clear?
2.  Which image asks it best?

#1

#2

#3

Toaster Remix

Dan's getting more mileage out of this problem than I am.  Either way, there are some good questions being asked re: pseudocontext, relevancy and so on.  So I'm curious, which one would you use and why?

(Note: don't check the answer until you've done the regression.  It's much more fun that way.)

The Original (setting 1,2 5 and 7)


Toaster Question from David Cox on Vimeo.


Or this?


Toaster Question (1-4) from David Cox on Vimeo.


Or this?


Toaster Question 2 (1-4) from David Cox on Vimeo.


The Answer


Toaster Answer from David Cox on Vimeo.

WCYDWT: Toast

Funny what you come up with when making breakfast for your kids.

Toaster Question from David Cox on Vimeo.

WCYDWT: Space Shuttle Discovery

I've tipped my hand here a bit because simply showing a shuttle launch would be way too open ended. I have the original lesson plan as designed by NASA and I'm pretty sure how I'd go about presenting this lesson, but I'm curious as to how y'all'd do it.


STS 121 Launch (Initial/Final values) from David Cox on Vimeo.
 

You Want Iteration?

...I'll give you iteration.

If the best thing is for students to actually encounter a situation that provokes a question  and the next best thing is to give them an image (static or dynamic) of said situation, then is the third best thing to give them an applet that models the situation?

Dan:

I only know I shot this because I felt like I needed it, because the alternative is a problem involving savings accounts with different principals and different monthly deposits and none of my kids have savings accounts.

Yeah, I'm not a big fan of the bank account problems either.  But I like race cars.  Lots and lots of race cars.  My students like 'em too.  Red ones.  And green ones. 

Since I don't know how to make the same guy show up on a picture/video in two different places and I don't really feel like going out to the park to run (a bunch of times), I figured I'd let the computer give me some iteration. 

So...

 What Can You Do With This?

Slide 1

Slide 2

Slide 3

                   

Applet's here.

Pizza Party!

I thought about giving this to my 7th graders...

Monday's Math Problem via @NCTM:

Batman and Robin each order a pizza. The circumference of Batman's pizza is 20 percent greater than the circumference of Robin's pizza.The area of Batman's pizza is what percentage greater than the area of Robin's pizza?

...for about two seconds.

But instead, I gave this:


What We Did

1.  Decided that the best question was:  Which pizza is a better deal?

2.  Misconception:  Comparing diameters to determine which pizza is preferable.  This leads to believing that two personal pizzas are a better deal than one large. (Note to self:  Let them think this as long as you can.  It's kinda fun and the truth hits them harder if they're committed to their initial opinion. )

3. Realized that area is the way we measure which one gives us the most pizza.

4. Determine area of each pizza and calculate $/sq".

5.  Sidebar:  Is $/sq" or sq"/$ a better rate to use?  Let them decide, but make them justify. 

6.  Extension: What are we really paying for?   Not the crust.  Assuming that the average pizza contains about 1" of crust on the circumference, removing it takes the personal pizza from $.14/sq." to $.28/sq".

7. Synthesis:  We brought out the laptops and put our data into Excel.  I allowed them to enter the diameter and cost for each pizza then showed them how to use the function and fill features to have the program do the number crunching for them.  I'm actually disappointed with myself for not doing this earlier in the year.  I often forget how powerful Excel is for teaching math. 

8. Conclusion: If you order a personal pizza, eat your crust!

9. Reflection  I wasn't prepared to handle the question on rates.  I think in terms of $/sq" and assumed that my students would too.  I also took an opportunity for student ownership away by drawing the two 7" pizzas inside of the 14" instead of allowing the student who came up with the idea a chance to shine. 

I'm taking this one on the road and will swap classes with other teachers in my department to see how their kids handle it. 

10.  What else would you have done with this lesson?

WCYDWT: Oranges

Oranges are packed and sold using a standard box...

 and contain fruit that is all the same size (kinda) based on average diameter...

which is determined using this:

They come in 10 sizes: 36, 40, 48, 56, 72, 88, 113, 138, 163 and 180 which is based on the number of pieces of fruit that can be packed in the box.