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. :-)

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.

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?

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?

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.

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!!!

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.

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.”

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.

Thanks for the props Mr. Meyer, I’m loving your blog.

Kate -if you’re using FireFox, try DownThemAll.

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