## What Can You Do With This: The \$6400 Question

I’m not claiming any kind of rigorous activity here. This is just a cute clip from Parks and Recreation, the best American comedy on TV right now, that begs one, maybe two good questions. I’ll throw this on an opener.

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What useful questions could we ask here?

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.

1. #### Jen

December 28, 2009 - 12:08 pm -

hmmmm…before I saw the whole clip I thought it might be about angles since it was talking about pool. But the first question that came to mind was how many games did they play so that he owed \$6400. Not sure how ‘high level’ that one is though! :)

2. #### Kate Nowak

December 28, 2009 - 12:13 pm -

This _is_ cute, and totally slipped by me even though I watch this show. Obvs there’s “How many games did they play?” Which in my experience the kids will want to make a little table and count the games and wash their hands of it… The question I have for you hs math teacher types is how to extend the inquiry into a compelling problem requiring the generalization (an exponential function). So they internalize and nimbly deploy that abstract tool in other situations. I’m not very good at that part. Good catch, Meyer.

3. #### Hemant

December 28, 2009 - 12:25 pm -

If they played 9 games, how much did they bet on the first game?

Suppose they bet \$25 on the first game. How many games did they just play?

If each game lasted 10 minutes, how much time did they spend playing pool? Is that realistic?

What’s the equation that would calculate the amount of money made in terms of games played?

If Mr. Meyer was the “failed architect” character, how many games would he have to win to match his teaching salary for the year? :)

4. #### Terry Kaminski

December 28, 2009 - 1:08 pm -

Great little clip!!! Just might have to show it to my Gr.12 students on first day back after Christmas break to get their minds going.

I like the questions that Hemant possed.

Thanks for sharing!!!

5. #### Dan Meyer

December 28, 2009 - 1:14 pm -

@Kate, at first I was like, “ohpleaseohplease let them have screwed up the math.”

I think Craig takes a brute force approach to your “how do we get them to generalize this?” question. I’m drawn more to Hemant’s final question, though, where you give a number large enough that tables would be drag and a half. (I’m not sure my yearly salary is that number, however.)

@Jen, you’re right. The question isn’t much more rigorous than “Solve: 25*2^(x-1)=6400,” except (1) the student has to develop the model rather than simply receive it and (2) whenever I have the chance to swap out a dinky opener problem for a cute excerpt from pop culture I tend not to think twice. Gimme, etc.

Hemant has the other question that occured to me: could you reasonably play nine games in a night? Take estimates from the class on the length of an average game of pool, compute, debate.

N.B. The jump cut to “… that would be \$6,400 … ” is so great. Kills me every single time. Watch Parks and Recreation.

6. #### D.C. Hess

December 29, 2009 - 12:56 am -

I would beg to differ. 30 Rock is the best comedy on American television.

What can you do with it? How ’bout using it as an opener for a discussion about the ramifications of non-commercial gambling? (For a social studies slant).

7. #### Dustin

December 29, 2009 - 7:40 am -

Dan,
I absolutely will spend as much time as possible going through your old posts. I have just finished my first semester of teaching Algebra II and Geometry after being an engineer for 15 years and am enthralled with your ideas and your approach. In fact, I am hoping it is not too late to tear down everything I did during the first semester and try to use your concept-based assessment techniques in the second semester.

Thank you.

8. #### Dan Meyer

December 29, 2009 - 2:45 pm -

@D.C., empirically speaking, The Office and 30 Rock have both had uneven seasons while Parks and Recreation has had the best sophomore season since, well, The Office.

Regardless, the fact that my top three ranking, as of today reads

1. Parks and Recreation
2. The Office
3. 30 Rock

with Community somewhere in the top eight, bodes really well for NBC right now.

9. #### John Spencer

December 30, 2009 - 4:30 am -

Finally, someone agrees. The best show on television. 30 Rock and The Office were both great. “Were” is the key. Now, it’s Parks and Recreation and Modern Family.

Anyway, I enjoy your blog. I’ve been reading it for some time. I enjoy the way you bridge the personal and the classroom all with the focus on learning at all times.

10. #### Carico

December 30, 2009 - 10:23 am -

I will have to check out the show. Sounds like it would be funny and I love a good laugh

11. #### Jeffery Heap

December 30, 2009 - 2:32 pm -

All great shows, television *gasp* is slowly getting better? Great blog sir!

12. #### Neel Patel

January 17, 2010 - 4:52 pm -

Dan, this clip was brilliant. I used it that first week back from break – 98% of my students were hooked and actually were doing some math!!! Just brilliant.

13. #### Cliff

January 23, 2010 - 12:13 am -

Ok, one of the big ideas that I can come up with is What are the possible first bets so that if they continued the “double or nothing” idea they would eventually end up at 6400 dollars?

That’s not an easy question, but leads toward a great idea about numeracy. The importance of prime factorization and uniqueness is something that continually passes our students by.

We hope that soon students would understand that to find all the possible solutions they should repeatedly divide 6400 by 2. This idea that they would surely come up with by themselves is one of the great ideas in algebra. That division is the opposite of multiplication is often taught, but multiplication by a half is often neglected. fractional multiplication causes problems, but it shouldn’t. Especially multiplication by quantities of the form 1/n.

This could lead in all sorts of questions, depending on the question asked.