## Tuesday, September 29, 2009

### The Very Exact Science of Guessing

When I picked up the book Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin by Lawrence Weinstein and John A. Adam, I expected a boring, academic tome that would be irrelevant for teachers, let alone students.

This would be about the time my mother would chime in gleefully, "Wrong again!"

Guesstimation is an excellent reference book for teachers looking to guide their students towards legitimate problem solving skills. A lot of the secret, as you might guess from the book's title, is in the oft-forgotten art of estimation.

The key chapter is the first one: "How to Solve Problems," which explains in simple language a two-step process:

Step 1: "Write down the answer," or in other words: Just take a guess! The authors stress that as long as you're within a factor of ten, you probably have a workable answer. Most every day problem fit into this: How long will it take to drive somewhere? How much might something you want to buy cost (or alternately, what can you afford)? At this point you might already have a good answer, the authors concede, but if that doesn't work, proceed to Step 2.

Step 2: Break the problem into smaller pieces and estimate each one. If you're wondering (as I was) how to teach this particular skill, I think the problems that populate the rest of this book would be excellent tools to do so. It's worth pointing out that authors prefer the geometric mean (something I think is rarely focused on in school unless you're taking statistics) for guesstimating the type of problems in the book.

In these first couple of chapters, the book also includes the best explanation and examples of both scientific notation and significant figures I've ever read in print. They're straightforward enough to use pretty much as-is, and it's worth at least borrowing the book from the library just for that section.

The rest of the book, the vast majority of its pages, are problems and solutions that require Guesstimation methods to solve. A couple of my favorite examples:
• What is the surface area of a typical human being?
• How much CO2 does one car emit into the atmosphere each year? All US cars?
• If all the pickles sold in the U.S. last year were placed end-to-end, what distance would they cover?
The topics covered in the remaining questions cover area, volume, speed, energy, algebra, geometry, physics, chemistry and more. Almost every problem requires some unit conversions, so this great practice for that skill as well.

How could I use this in class?

You should start by giving some of the problems and their included solutions to the students as a guide an introduction. You could also provide the lists of useful formulas and items to compare things to from the appendices. Then, you have two fairly easy routes to choose from:
1. Give students one of the "unanswered questions" included in the back of the book.
2. Have students create create their own (and solve them).
Students should absolutely work collaboratively on these kinds of problems. Give them chart paper or a similar large canvas on which to illustrate and explain their solutions (AVID teachers will love this!). Be sure to have groups present to each other. It would be interesting to have an entire class working on the same problem or two with the explicit idea that answers will be quite different and often very unique.

In general, Guesstimation provides a great, easy-to-follow guide on introducing skills that are sorely lacking in school: problem solving and critical thinking. These are the kinds of skills that will help students do better on standardized tests (if you're into that sort of thing). I recommend this book for any high school (or Honors/Pre-AP middle school) math or science classroom.

Dave @ Home School Dad said...

I just ordered this from my library. I guestimate I will have it within a week. Thanks for suggesting it

gb said...

"...as long as you're within a factor of ten, you probably have a workable answer. Most every day problem fit into this: How long will it take to drive somewhere"

So if I guess it will take me ten hours to drive to visit a friend (quite doable in a day, drive back the next), and it actually takes me a hundred hours - you gotta sleep, eat, shower and stuff and even if I drive 12 hours a day, it's still more than a week) - I've missed a week's work and gotten fired, and I've still got to spend a week or more driving back again before I look for a new job.

There are times when being out by an order of magnitude isn't actually "workable" - and the first example looks like it's exactly one of those.

Mr. D said...

gb: If I wasn't clear, I was stressing that the everyday problems I listed were best for a "just take a guess" approach, and that the factor of ten would come in to play when you used that guess as part of a bigger problem (such as the ones that make up the bulk of this book).

Yet your example doesn't really jive with what's explained in Guesstimation anyway:

Following the book's idea, if you had already guessed it would take you 10 hours to drive somewhere, that means that in all likelihood your actual driving time should be somewhere between 1 and 100 hours. You would be factoring that into your planning from the beginning, not throwing your hands up because it was that far off afterward!

Also, to expand on what's explained in the book, I believe the authors would give you several suggestions to make your initial guess more accurate:

1. Compare your trip to a trip you've already taken that you believe to be about the same distance
2. Perhaps you know example how long it would take to drive part of the distance. You might consider that a quarter or a third of the trip, then use that to find a range for what you might actually expect.
3. Use a tool like an online map, which we know is never completely accurate, but gives us another reasonable guess based on the distance and a series of assumptions (that you will drive the speed limit, won't make any stops, what traffic will be like, that there will be no unexpected delays due to construction, nearby special events, accidents, etc).

In fact online maps and trip planners like MapQuest and the like are a perfect example of a Guesstimation method at work. They make a series of reasonable guesses that factor into the final driving time they give you. We all look at these assuming they are just an estimate, and plan accordingly (usually in case it takes more time).