## What Can You Do With This: The Bone Collector

The math here is fairly self-evident (I think) but I’m really curious how you’d deploy this in the classroom. Be specific.

BTW: Mr. Follett â€” concise and correct:

(1) Play clip.
(2) Pass out the photograph, Iâ€™d get this by doing a screen grab.
(3) Make other materials available: dollar bills, rulers
(4) Make this info available.
(5) Ask them the shoe size.
(6) Discuss, reflect, justify.

This is, more or less, exactly how it went in Algebra for us this week. Here is the relevant frame grab formatted as a 4×6 frame as well as the follow-up scene from the movie itself.

BTW: The application RulerPhone ties into this nicely. More here.

BTW: A much better hook from an audience member at my UC Berkeley presentation than the one I originally concocted: “Which of your classmates could be the killer?”

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

1. #### JasonP

October 8, 2008 - 4:38 pm -

Mood………..I’d use it for discussion on how the director creates mood…what is close-up? What is far away? What details are being paid attention to? That lest question allows a link to a possible reading assignment.

2. #### Kate

October 8, 2008 - 5:03 pm -

I can see two places to use it: the more obvious algebra 1 with the application of proportion, or geometry around a discussion of what it means to measure something.

I can also see two ways to use it – as simply a more interesting way to state a problem than text-on-paper or text-on-wall.

Or, more fun, give it to them cold. By 9th grade they are no strangers to linear/proportional reasoning. A lesson that starts with “what is going on here” and ends with kids figuring out the length of the footprint and/or shoe size. That wouldn’t take them that long. Oooh! Length vs shoe size would be a nice direct variation, too. (I think…is that linear? Would a regression go through the origin? Must investigate.)

And then extends to measuring all kinds of stuff with dollar bills, and then measuring stuff with other stuff… How many paper clips long is your shoe? How many mechanical pencils long is your shoe? Your height? This classroom? Someone will notice it would be easier to measure the classroom with meter sticks than paper clips, and then convert to paper clips. (Here we see who never really “got” multiplication.) How does this change if we are talking about area? How many dollar bills cover the surface of your desk? The classroom floor? What other shapes tile a two dimensional surface? What shapes completely fill a three dimensional surface? How many would it take to fill up this room?

Ahem. I probably wouldn’t take it that far. But I like the clip. It’s going in the file. :-)

3. #### dan

October 8, 2008 - 5:10 pm -

Okay. W/r/t proportional reasoning, once you play the clip, what do you have the students do? How do they get their hands dirty here? This part is important.

4. #### Steven Peters

October 8, 2008 - 5:13 pm -

There’s the improvised use of a dollar bill for scale in crime scene photographs. I’ve also seen coins used for scale in pictures of small things.

There’s potential for abuse of this concept if one happens to have an oversized or undersized dollar bill or coin. A funny story I heard is about a geology grad student who used an pencil for scale in pictures of small geological features in her thesis. As a joke, she took a photo of herself with an oversized 3-foot long pencil captioned “Pencil, human for scale” and put it in the appendix. I believe she had to remove it before she could graduate.

A geometry ratios problem would be finding the dimensions of that footprint using the relative size of a dollar bill.

A trig problem would address the effect of perspective on the photograph. Taking a photo from an angle not directly head-on can cause distortion of the shapes. For example, a dollar bill has an aspect ratio (length / height) of ~2.36. By changing perspective it could appear to be a square with aspect ratio of 1, or very slender with a larger aspect ratio. Show a dollar bill with a different aspect ratio and ask what the camera angle is that generated that picture.

5. #### Steven Peters

October 8, 2008 - 5:17 pm -

Whoops I posted before I saw the other comments.

Dan, I think the first thing they have to do is get a ruler and measure a dollar bill. Do they get a printout of the picture? If so, then they should take the ruler to the printout and go to town.

6. #### dan

October 8, 2008 - 5:38 pm -

It’s your class, Steve, you make the rules. Ideally, in our classroom presentation of the problem, we’ll spend our resources on challenging, interesting things. (Making the kids rent the movie would be spending resources on an easy, boring thing, for one example.)

I like the trig application.

7. #### Todd

October 8, 2008 - 8:48 pm -

I’m stretching…

* Rising action (though the scene might need more set up for that) – get a group of kids to write up what happened just before this scene and another batch on what happens after it. Do what you can to break out the different elements of plot going on here, mapping things out on a Freitag’s curve.
* Logic (how many of your students would know right away why she set the dollar bill down on the ground?) – this is another chance to work on deductive reasoning, where students have to figure out why she’s doing what she’s doing and use evidence from the clip to back up their ideas.

If I taught Film:
Storyboard this scene (weak).

And if I taught Photo:
Recreate the closing shot with other images used for scale, some real and some misleading, similar to what Steven suggested.

8. #### Kate

October 9, 2008 - 4:19 am -

Well, ok, planning out mechanics of how something is going to go down isn’t really something that I’m good at. But I sense that that is your point – this is a thing that many teachers need to work on.

My class sizes are 20-30, and though we move around, my desks start out arranged in pairs, all facing forward. So here’s how I’d work it, not that it’s the best way:

“Let’s watch a short clip that’s a little mysterious. When it ends, I want a short explanation of what you think is going on here. Discuss it with your neighbor and be prepared to share.”

Play the clip. Let them talk a minute, then call on 2-3 students to explain what they think is going on. Play the clip again if they need it, or if the discussion prompts disagreements about what happened. This year I have a kind of oppositional group who will probably insist that she is obviously mentally challenged because she should just go get a ruler and come back later.

Possible questions depending on where the discussion goes. Why did she use US currency and not something else, like a pen? Why did she send the kid to buy a camera? Why would she want to take a photo? There are probably lots of other things one should ask here, but that’s what this exercise is for, right?

Once everyone is on board with the idea that she could use the photo to figure out shoe size later and as an evidence record, I would pause the frame featuring the footprint and dollar bill. Ask the kids to pull out any small bills they have, and ideally hand each pair a color printout of the frame (handing out different sized photos to different groups would be cool) (is that even possible? I’ve never tried printing a still frame from a video) and a length to shoe size conversion table. They know where the rulers are.

I’d circulate and see what different methods were being deployed. I’d ask a few kids who took different approaches to write their solution on the whiteboard and present it to the class. I’d ask the class which solution they liked the best and why. I would favor the efficient, elegant, and algebraic.

Then I’d give them a worksheet where they can use proportions to solve word problems and find sides in similar figures. I would do 1-2 examples with them, have them work on the rest, and complete any they don’t finish for homework.

How would other people do it differently? What opportunities for deeper learning am I missing?

9. #### BC

October 9, 2008 - 5:15 am -

In a perfect world, where every student has access to an iPhone or iTouch, you could show the clip, let the kids flounder around with any of the above ideas, then have them whip out their iPhone with the rulerphone app which allows you to measure any object by taking a picture of it. Only thing is you must put a standard sized credit card in the picture. Wonder why?

10. #### Michael

October 9, 2008 - 7:08 am -

Anyone curious how many seconds each camera angle is? Why did the foot print get more time in the clip than the bolt and crushed powder? Does the time a director chooses to stay on a certain camera angle tell the viewer something about the importance of that piece of the movie? How could you accurately time each piece with everyday tools?

Take it to the next level – what is the average time for each angle? If we did this for a variety of different clips, what can be said about modern directing and movie making? What if you included movies before the 1980’s. Is there a significant change in how long a camera angle is? What do you think is the cause of this change?

11. #### Tom

October 9, 2008 - 7:25 am -

I wonder if you couldn’t work a scam element into it.

Here’s the footprint (if you were really into it- give them a plaster cast of your own footprint or just a photocopy on a piece of paper).

Here’s a dollar and a camera.

Now the student task is to frame the following individual (whose shoe size does not match- obviously) by distorting the perspective of the dollar by raising it/lowering it vs the shoe. They figure out how high/low it has to be to frame their man.

Now based on that data- how high or low would it need to be to frame individuals with shoe sizes of X, Y, and Z.

I’m assuming you’d have to have fairly big difference or the gradations in height might be too fine.

Once again, no math guy, but seems like that’d be graphable and pretty entertaining.

12. #### Jovan

October 9, 2008 - 2:37 pm -

I teach 8th grade and I love the geometry in the opening.

Initially, I saw plenty of triangles and parallel lines in the bridge structure. We have right triangles, what appear to be equilateral or isosceles depending on one’s analysis of the shot.

We’ve got plenty of alternate interior angles, congruence, etc going on there.

The proportionality concept also presented itself ( pretty obvious I think ) when the dollar bill was placed next to the foot print.

However, if we assumed some things about the triangles ( angle measure, length of a side, congruence ,etc) I think some pretty interesting problems could present themselves.

We’ve got the Pythagorean theorem, area, perimeter, etc.

If we assume that the structures are squares or rectangles we can determine the lengths of the diagonals within those structures.

13. #### Mr Follett

October 9, 2008 - 5:20 pm -

(1) Play clip.
(2) Pass out the photograph, I’d get this by doing a screen grab.
(3) Make other materials available: dollar bills, rulers
(4) Make this info available.
(5) Ask them the shoe size.
(6) Discuss, reflect, justify.

14. #### Druin

October 10, 2008 - 5:43 am -

This is perfect for me to use next week actually as I start linear regression in stat. We will measure our shoeprints and our heights and see if we can make a prediction for the height of the perp. If it’s non-linear, then we be able to stretch it out a few weeks until we get to non-linear regression.

Thanks!!!

15. #### Jeremy

October 10, 2008 - 5:56 am -

Some pretty cool ideas. I’m a big fan of the trig app, linear regression, but really think the scam idea could be pretty entertaining/educational as well.

16. #### Christopher

October 10, 2008 - 8:15 am -

From an ELA slant, I would look at how the director uses direct characterization and indirect characterization. The clip is cut at a point where the students would be left to wonder about the relationship between the police officer and the boy, wonder if the boy respected the police officer’s request, and wonder about the police officer’s level of experience (and why she’s alone and on such a shoestring budget). What can we deduce about both characters in the short clip? What does the setting say about the boy? This clip would provoke a very interesting conversation that could develop into a discussion on respect for authority, race relations, or resourcefulness.

17. #### Darren Draper

October 10, 2008 - 12:38 pm -

Jovan and Mr. Follett are good here and on the right track but I’d do a combination of the two.

1) Put ’em in small groups, 2 or 3 per group, sharing a laptop – but don’t tell them anything about the clip ahead of time.

2) Make it a contest and an assignment: The group that identifies the most legitimate ties to geometry in the clip wins. Wins what? Doesn’t matter. One point per geometry tie, Jovan’s made a good list of answers.

Very important: From the beginning, you’ve got to make it clear that there are at least 15 decent ties to geometry. Make them set their sights high.

3) The laptop’s for the bonus – and for the kid in the group that can only see triangles and a cop in the opening scene.

Five point bonus: Name the movie, its rating, the year it was released, and the names of the two actors in the scene.

Make the assignment out of 20 and you’ve got yourself an engaged classroom and a room full of teenagers that will dream of geometry the next time they meet with their parole officer.

One caveat: Close the door nice and tight before showing the video because your principal’s not gonna like the idea of an R-rated movie in geometry class, regardless of the length of the clip.

18. #### Darren Draper

October 10, 2008 - 12:41 pm -

I forgot to add that Mr. Follet’s addition is homework. With the screen cap and link to shoe sizes, the kids can find the rest of the stuff they’ll need at home.

Plus it’ll make great dinner conversation.

“Mom, can I have a dollar? I’ve gotta do my geometry homework.”

19. #### dan

October 10, 2008 - 4:02 pm -

Good stuff all around, but Mr. Follett’s work, in particular, is well-planned. I have updated the original post to add a file and reflect the c.w.

20. #### sam shah

October 11, 2008 - 5:49 pm -

Love it. The only thing I’d follow up with is:

Is the shoe size the same as anyone in the class? Is anyone a suspect?

Mwa hahaha.

21. #### Tim

October 12, 2008 - 11:47 am -

First off, that boy in the clip looks a heckuva lot like a younger version of you, Dan.

22. #### Kate

October 18, 2008 - 6:02 am -

23. #### Candace

January 23, 2009 - 1:15 am -

Hi Dan,

I’m going to attempt to use this as an activity for my Geometry class as part of a quick brush up on proportions before starting similar figures…assuming the projector I just borrowed is compatible with my laptop.

I was also considering using it for my Algebra I class, but was curious how far into proportions do you generally get before you use this? Do students already know how to solve problems involving proportions or is this generally more of an exercise to get them to use proportional reasoning before you’ve officially taught them the procedural way to solve proportions?

– Candace

24. #### Dan Meyer

January 23, 2009 - 7:51 pm -

Good questions, Candace, and not ones I feel confident answering. I used this in Algebra 1 at the end of our proportions unit. I didn’t scaffold the clip at all, just played it, passed out their own photos, and told them to have a good weekend. I think I mentioned at my session that this didn’t end well.

So I don’t have a strong opinion one way or the other vis-a-vis when you use it and in what class. I know, though, that I’ll make it an in-class activity next year. I’m curious how it ends up for you, if you feel like dropping me a line.