## [3ACTS] Popcorn Picker

See the task page.

FWIW, this is exactly the reaction I hoped to provoke with that video:

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This is a classic textbook problem that we actually did early in the year (Discovering Geometry, Ch. 10) and at the time I recall a number of students asking me for help. They weren’t entirely sure what the problem was asking, and they didn’t know where to start. I’m sure a large number of my no-homework doers saw a block of text and skipped it entirely. We did this today, and kids totally bought into it.

This was awesome. I just showed my 8 year old and asked, “Which one will hold the most popcorn?” He answered, “Both.” I now need to show the other kids.

2012 Jun 16. From Discovering Geometry, Fifth Edition, pg. 548:

If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two longer sides together, you get a tall, thin cylinder. If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two shorter sides together, you get a short, fat cylinder. Which of the two cylinders has the greater volume?

2012 Jul 2. From Everyday Math. Page One. Page Two.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

### 16 Comments

1. #### David Wees

June 4, 2012 - 7:38 am -

I think I’m going to use this with my staff, thank you so much. I heard about it Saturday from two very clever numeracy helping teachers (thanks Chris and Marc) and think it could be a great jumping off point for talking about how important it is to challenge misconceptions (volume = surface area is a common one) our students (and staff) have.

2. #### Ryan Brown

June 4, 2012 - 9:28 am -

A colleague of mine and I also did Popcorn Picker today with kids – great review problem for volume, area, circumference as we prepare for final exams.

Dan, this is one of your best. It’s so simple, yet conveys a very obvious first question that engages students in the mathematics at a very accessible level. This is a classic textbook problem that we actually did early in the year (Discovering Geometry, Ch. 10) and at the time I recall a number of students asking me for help. They weren’t entirely sure what the problem was asking, and they didn’t know where to start. I’m sure a large number of my no-homework doers saw a block of text and skipped it entirely.

We did this today, and kids totally bought into it. Dan’s silly grin was the icing on the cake (or the butter on the popcorn!) They knew from the look on Dan’s face alone that we had the right answer.

3 Acts and 101qs are brilliant for this reason. When a simple video or picture has a question that is just begging to be asked, student interest and engagement skyrockets. And to echo what @yaacoviland stated, this engagement allows us to dig deeper and expose misconceptions that even the brightest students have.

I’m pumped, the kids are interested (and it’s June 4th and humid!), and other classroom down the hall are working on review packets.

Keep pushing us Dan!

3. #### Mary

June 4, 2012 - 9:32 am -

I saw a similar activity on Thinkfinity and did it with my students last year and allowed the students to eat their experiment. They loved the activity.

4. #### Fawn Nguyen

June 4, 2012 - 11:01 am -

I did this with my 6th graders, BUT we folded the popcorn “containers” (bottomless) into rectangular prisms. We’ll definitely graduate to the cylinders. Ha, graduated cylinder… yea. Thanks, Dan.

5. #### Andy Martinson

June 4, 2012 - 11:18 am -

Did this with kids today–went great. The greatest part of the problem was that in the end, your 3rd act showed that the actual calculations were not the only way to answer a question like this; while I wanted them to find the two different radii, the kids who found and used the diameter of the cylinder rather than the radius still got the same “answer” to which has more popcorn. We then had a great discussion around why that still worked out for us. The incorrect numerical answer yielded the correct answer. That’s a great math problem to discuss.

My favorite comments were “is he grinning?”, “is that the same guy who was shooting baskets in that other video?”, and then some advice: “the one on the right should have looked over at the bigger pile and frowned.

Another kid said “you should make videos like this for all our problems.” I responded: “why? I can just use em from this guy.”

Maybe after their final Thursday I’ll show the one-act of you showering to test if they still think you’re cool.

6. #### Richard Strausz

June 5, 2012 - 4:24 am -

Every year we have ‘popcorn day’ during the volume unit in geometry. I build it up all year long: “yes, we are going to fill the classroom with popcorn and you will have to eat your way out.”

On the day, I bring in an airpopper and a container and start popping. As the batches are done and the students eat, we explore the questions of how long it would actually take to fill the room – very long… – and how much it would cost – lots of money…

7. #### brooke

June 6, 2012 - 1:35 pm -

This was awesome. I just showed my 8 year old and asked, “Which one will hold the most popcorn?” He answered, “Both.” I now need to show the other kids.

8. #### Sam

June 6, 2012 - 8:45 pm -

I like this problem a lot.

I’m curious how people use something like this. Are you going to put it into a unit about volume? Is it something you do when you focus on problem solving? At the end of solving this problem what do you want your students to have learned? Do you build on this learning the next day? How?

9. #### Scott

June 7, 2012 - 6:58 pm -

Again, a well distilled version of the video-question.

One to put in your portfolio.

10. #### K.R.

June 12, 2012 - 5:50 pm -

I love this problem!

I did something like this on the second day of the volume unit in a high school geometry class. I knew they had seen the volume formulas for prisms and cylinders before, but this provided some motivation & interest (not to mention mathematical thinking) rather than just “practice finding the volume of these prisms.” I found the Illuminations site on this helpful:
http://illuminations.nctm.org/LessonDetail.aspx?id=L797

11. #### Fritzky

June 12, 2012 - 6:45 pm -

Without a doubt I loved this lesson. I used this lesson after a unit on surface area but before I started volume, not sure if that was the best time but it seemed to work well. I teach a 5th grade inclusion class it took the students 75 minutes to solve this problem and when they did their confidence was contagious. Can’t thank you enough Dan.

12. #### L.C.

August 3, 2012 - 7:31 am -

I love this lesson. I have done a version of this with my 8th graders for the past 3 years. I have used the lesson from NCTM Illuminations that K.R. mentions above (http://illuminations.nctm.org/LessonDetail.aspx?id=L797) and called it “Popcorn Prisms.” I make the popcorn fresh in a microwave in the classroom, so the kids are immediately hooked by the smell (“Oooo, do I smell popcorn?”) when they walk in the door. In this lesson you put the taller prism inside the shorter. Then you fill the taller with popcorn and lift it away. Most students predict that the popcorn will fill to the top of the shorter. And when it doesn’t: mind = blown.