## [3ACTS] Car Caravan

If you find that first act perplexing, feel free to follow up on all three. Four other notes:

• This one pairs nicely with the ticket roll problem. Try to imagine the tickets as really, really thin cars.
• In the second act, I offer this picture of a single Matchbox car. There aren’t any measurements and it bears perhaps only a passing resemblance to any of the cars in the picture. I like these moments a lot, though. The student has to estimate the dimensions of the car. Her estimate is entirely her own and will likely differ from that of her classmates. Everyone will own a different answer, then, even though they’ll all be developing proficiency with the same mathematical tools. Everybody wins.
• If you’d like to keep track of all the three-act tasks I’ve released so far, I have them logged in this spreadsheet, which is really insufficient but there it is.
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. #### Ben

January 4, 2012 - 5:54 am -

I see what you did there with the link to the Common Core, a very masterful stroke, nicely done!

Thanks for including the link to the spreadsheet of “3 acts” you’ve created, will be something useful to share with other teachers.

2. #### Michael

January 4, 2012 - 9:15 am -

So why do all that math when I can just count the cars?

Now, let’s do error analysis on your long distance counting!

3. #### Michael

January 4, 2012 - 10:12 am -

Another sequel?

How many cars are on the outermost ring? (Ask again for 10,000 car and chalk drawing sequels.)

Dan, thanks for putting the Three Acts spreadsheet together. To make it easier to share with other teachers, I added it to bitly and customized it to bit.ly/meyerlist

I hope that’s alright.

Cheers!

4. #### John Berray

January 4, 2012 - 11:50 am -

I was glad to see the “Three-Act Math” section under My Curricula pop up on your blog. It’s interesting to follow the evolution of the WCYDWT/#anyqs /3act math over time through your posts.

I’m still curious about how long you think you would spend with a typical class on a problem like this Car Caravan? I know it depends on the class and the discussion, but ballpark.

5. #### louise

January 4, 2012 - 2:58 pm -

My first thought was that here is a boy worse than my own, how much did Mommy Dan have to spend to satisfy his desire for toy cars? (I am glad for her sake that they are apparently not yours)

6. #### Daniel

January 5, 2012 - 8:37 am -

As a math teacher from Ontario, Canada I love what you are doing Dan. These lessons are fantastic and engaging. However, I teach grade 3-8 kids math and was wondering if you or anybody else has created great problems like this for kids not yet in high school. We are reforming our teaching of math in our Province and this is another great way to get kids, all kids, loving math.

7. #### Dan Meyer

January 6, 2012 - 6:32 am -

John:

It’s interesting to follow the evolution of the WCYDWT/#anyqs /3act math over time through your posts.

I think so too. It’s been a real iterative process, one that you folks have been tightly tied up in with your feedback, criticism, and comments. It would have taken me ten extra years to get to this place if I didn’t have you guys setting me straight so often.

John:

I’m still curious about how long you think you would spend with a typical class on a problem like this Car Caravan? I know it depends on the class and the discussion, but ballpark.

At the moment I don’t include timing on my three-act posts in large part because I think you’d have a better idea than I would what resources your class would need to participate in this kind of investigation, including time. In my class, I suspect we’d finish this one inside thirty minutes. I can easily see another classroom taking more time with it, though.

Daniel:

I teach grade 3-8 kids math and was wondering if you or anybody else has created great problems like this for kids not yet in high school.

Hi Daniel, thanks for the feedback. This question comes up kind of a lot and I don’t have an answer. I’ll commit some more time to an investigation and get back to you.

8. #### Daniel

January 6, 2012 - 6:39 am -

Thanks Dan, in all reality I am looking at creating some of my own but was looking for something to work against. Look forward to seeing you speak in Kingston in May!

9. #### Sarah

January 6, 2012 - 8:45 am -

I’ve been a guest teacher for a year and find math classes the most difficult: boring curriculum…disengaged students…horrible behavior. I’m excited to add these 3-acts problems to my bag of tricks. It works wonders when I can throw them off with something weird. Of course, standing at the front of the class doing deep Yoga breaths works too but it’s not really math related.

10. #### Michael Fenton

January 6, 2012 - 9:36 am -

Working on this problem with a group of teachers. Here are some suggestions for more sequels:

1. How many cars of each color are there?

2. How many cars are in the longest ring of each color?

3. What size square would you need to fit the 2500 cars? (Answer in cars, in, or cm?)

4. What would be the diameter of the circle containing 2500 full-size cars? (Pick your favorite vehicle—Hummer, Prius, etc.—or go with the 1/64 ratio printed on the bottom of the matchbox car.)

5. How many cars would fit on a student desk?

6. How many cars would fit in a regular (or compact) parking space?

7. How many cars would fit on the classroom floor (area)? Or in a school bus (volume)? Or in a car?

11. #### Dvora

January 7, 2012 - 10:06 am -

My students loved when I did the penny pyramid with them. It took a couple of class periods as they insisted on more time to calculate.

I am currently working on graphing and have been using graphing stories with them. I think this would be a good one to bring in along with the ticket roll.

Thanks for sharing all the wonderful work you are doing.

12. #### Sue VanHattum

January 8, 2012 - 9:56 am -

My son is a Hot Wheels fanatic, and will love this picture. I don’t plan to do anything more than show him the picture. I’m wondering if he’ll take the bait and put his own cars in this arrangement. I’ll post a photo if he does.

Thanks!

For classroom use, it should be noted that this problem will appeal to more boys than girls. It’s important to be aware of that dynamic and offer plenty of problems that will appeal equally and to find a few that appeal to more girls than boys.

13. #### a different eric

March 6, 2012 - 4:33 pm -

My kids are slowly catching on… I think.

Today, after warmups, my next slide was this picture. One of my 8th grade girls covered her eyes very quickly and said, “Nooooooo… I don’t wanna know ANYTHING about that picture!”

I replied, “Well… let’s just leave it up to the class then!” With a big smile. I had each group come up with a question they would like answered.

1. How many colors are there?
2. What is that picture made up of?
:: I’m starting to roll my eyes ::
3. How much did this cost?
:: I secretly smile as no one sees this as a problem ::
:: Funny-boy pipes up::
4. How many CARS are there??::
:: Class moans, why did you ask him that?!::

“Okay, guys… I won’t take question number 4. I’ll take question number 3. That sounds interesting to me.”

It only took them about, oh… maybe 2.5 seconds realize what they just did.

It’s always more fun than they admit. I’m starting to think that if I showed movies and ate popcorn everyday, 8th graders would complain about either the movie I chose or the way I popped the popcorn.

14. #### MRhodes

March 8, 2012 - 4:35 pm -

Use this image to find the area of the pentagon…..

Another good one was the NYC Supreme Court building which is in the shape of a hexagon from an aerial view.