How to develop "number sense"

April 15, 2009 10:53 AM

How might a person go about cultivating "number sense"? I mean something different from abstract reasoning. I'm asking how one might develop an intuition for physical concepts such as numbers, lengths, and sizes. Examples might include knowing how many people went to your school, how many yards away is a given building, how large is your apartment, how much does the average American earn, etc. These things could be measured or found out through research, but how might a person develop the ability to give reasonable estimates?
posted by Busoni to science & nature (22 comments total)

You have to do it repeatedly and develop a basis of comparison (i.e. football field, length of your stride). For example, pace off the width of a city street so you know what that looks like. Measure the length of your hand, or the height of a basketball hoop so you can compare an unknown to a known. So if something is two hand lengths it's 16 inches or whatever. The important thing is practicing the skill and determining your accuracy.
posted by electroboy at 10:59 AM on April 15

Sometimes there are rules of thumb you can follow. For example, if you estimate the angle of a curved surface (a hill, let's say), people tend to overestimate it by about 15 degrees. So figure out what it looks like to you, subtract 15, and you're probably pretty close to what it actually is.

I once read a similar thing that biologists do when estimating herd sizes from helicopters. They'd take their best estimate and then multiply by 1.5. Sorry, can't recall where I saw that.

In general, though, the answer is you get your number sense by dealing with that particular measurement on a routine basis. A professional realtor can probably walk through a house once and give you a good estimate of how many square feet it has, because they see those things every day. I'm a lot better at estimate feet & inches since I started building furniture (although once it gets over ten or fifteen feet I'm no better than I ever was).
posted by echo target at 11:02 AM on April 15

A good place to start is Innumeracy by John Allen Paulos; he has written a number of other books along the same line that you might find helpful. This recent MeFi thread might be helpful as well.
posted by TedW at 11:02 AM on April 15 [3 favorites]

I've always had strong abilities in this area and I think it just comes from constantly being aware of quantitative aspects of things in general (working things out when possible) and having a memory for the details. Not many people actually are interested in the length of a room or the height of a tree, but for those people who actually work out some figures regularly, especially when they're young, it leaves cumulative impressions that develop that sense. Abstract curiosity is probably what drives that kind of thing.
posted by crapmatic at 11:02 AM on April 15

One summer I went on a trip with my Audubon/conservationist/birdwatching friends, and they were learning how to estimate the size of bird flocks from more experienced buddies. They would guess the number immediately after seeing the flock, before having had the time to think about it. Then they would take the time to actually count the birds as accurately as possible and see how their guess compared. The next time they saw a flock, they'd know if they had a tendency to go over or under and correct for that particular size. After a year or two of doing that, people appeared to have no trouble correctly assessing the exact count of birds ("42"), or at least give very reasonable estimates for larger numbers. I was incredibly impressed, but all of the birdwatchers had learned to do it through practice.

I'm guessing you could start doing that with all kinds of things around you?
posted by halogen at 11:03 AM on April 15 [1 favorite]

Start with this previous list of tips and tricks

Those, plus a few common conversion factors help out a lot. Then, just practice. Try to calculate the volume of the Empire state building, for example. (Note that I've never been there, so these numbers are made up)

Well, it's a whole block, and there are about 20 blocks to a mile.
A mile is about 5000 feet, divided by 20, means that it's about 250 feet square at its base
A story is about 10 feet and it's around 100 stories tall, so that gives dimensions of 250x250x1000 = 62 million cubic feet. Lop a chunk off because it narros as it rises, and let's call it 45 million ft^3

After doing this, I googled it, and the first result lists it at 37 million feet, so our estimate wasn't too bad.

Also try googling "back of the envelope calculations" for more little tips.
posted by chrisamiller at 11:04 AM on April 15

I have the GPS in my car set to give directions like "in 100 yards, turn left" (except it's Eddie Izzard's voice, so it goes "in 100 yahhhhds, turn left") instead of "turn left on Aurora." It's helping me get a grasp on distances, something I've always been shaky at.
posted by The corpse in the library at 11:10 AM on April 15

I worked in a warehouse in inventory control in high school. Had to count every fuckin' box in the joint. I learned to multiply by weird numbers (23, the number of biscuit cases per layer on a pallet), as well.
posted by notsnot at 11:13 AM on April 15

Seconding reading the work of Paulos.
posted by box at 11:19 AM on April 15

You have to do it repeatedly and develop a basis of comparison

This is true. After many years of knitting, I can estimate measurements under 24" quite accurately (and I learned long ago that my handspan is exactly 8"). Sometimes it just helps to have a good frame of reference, though. I am good at estimating men's weights because I have three brothers and a father who are all very different sizes and I just take the closest comparison and adjust it.
posted by orange swan at 11:23 AM on April 15

Nthing that it's mostly practice, so long as you regularly check your guesses against reality so that you can refine your intuition. Once, when I'd been doing a lot of precision machining, I was able to guess the thickness of a dime within a thousandth of an inch. A friend who grew up doing construction work with his uncles can stand in the middle of a large room and tell you it's dimensions within a foot or so. For us it was just everyday familiarity with what certain dimensions looked like - there was never any abstract theory involved.
posted by jon1270 at 11:30 AM on April 15

Print off these xkcd comics and put them up somewhere where you'll see them often (fridge, toilet or similar), as a way of building up your 'common sense' feeling for the sizes of things. You can even get the first one as a poster.
posted by Acheman at 11:30 AM on April 15

OK, I just noticed that 'Depth' doesn't have any actual numbers on it. But the other two would still be fit for purpose.
posted by Acheman at 11:32 AM on April 15

Seconding Paulos's excellent book Innumeracy. It answers your exact question. A must-read.
posted by Jaltcoh at 11:50 AM on April 15

And if you want something more focused on being skeptical toward info about numbers fed to you by the media, get Paulos's A Mathematician Reads the Newspaper or read his columns.
posted by Jaltcoh at 11:52 AM on April 15

Another "experience" anecdote. I worked in a small bakery we had to weigh each loaf of bread dough by hand and timed the baking in our heads. After a few months I could pick up something under 5 pounds and guess its weight within an ounce and time anything under an hour with pretty alarming accuracy.

Pretty much any woodworker can judge distances from 1/16" to yards pretty accurately. Golfers are pretty good at longer distances in yards.

I'd do three things:
1) Familiarize yourself with conversions. Not just "rods to an acre" stuff but real world representations of an acre, gallon, cubic meter, etc.

2) Find a hobby that uses lots of measurements, or start using/paying more attention to measurements in an existing hobby. You can use measurements all the time in everything you do, just become more aware of them. Baking, sewing, woodworking, scrapbooking, BBQing, driving, walking, drinking...

3) Play guessing games with yourself. Get a ball of string and guess how long an inch/foot/yard is, then measure it to see how far off you were and in what direction. Guess how far it is between two places and then measure it on Google Maps. Buy a bag of M&Ms and guess how many are in the bag, then count them. Set a timer for an hour and try to check it every 10 minutes. etc. etc. etc. You'll find very quickly that you'll get much better at all of these things.
posted by Ookseer at 12:02 PM on April 15

Back in the day when I was a track and field athlete, I had to do lots of training schedules with sets of sprints of varying distances. And once you know how long two hundreds meter can be, especially after you've just run three hundred at full speed, you'll never forget that.
posted by ijsbrand at 12:08 PM on April 15

There is an interesting book called 'Consider a Spherical Cow' by John Harte that goes through this process. I am reading/working my way through it. It basically starts off each page with a question such as "How many shoemakers are in the US?" and then goes through the process of estimating it.

It is targeted at environmental engineers, but I'm not one, and like it.
posted by a womble is an active kind of sloth at 12:44 PM on April 15 [2 favorites]

I used to do inventory in hardware stores. If you have a bin of metal rods, for example, count one small section. Now count how many sections of that size are in the entire bin. Multiply. Practice by counting the entire bin one by one and see how close you were.
posted by cda at 12:53 PM on April 15

I am surprised it hasn't been mentioned yet, but I find the MegaPenny project (as seen on mefi!) a good guide to very large numbers whenever I encounter them in the press.
posted by TedW at 3:33 PM on April 15

I have the GPS in my car set to give directions like "in 100 yards, turn left" (except it's Eddie Izzard's voice, so it goes "in 100 yahhhhds, turn left") instead of "turn left on Aurora." It's helping me get a grasp on distances, something I've always been shaky at.

The GPS probably isn't helping you with that.

With my TomTom GPS (as well as the Garmins my dad uses), those close-distance announcements are made at entirely the wrong time. So, if you have it set to announce the turn in 100 yards, and you're doing 60mph, I've found that it'll tell you to turn in 100 yards when you actually have about 50-75 yards.

Now, if you got yourself a handheld GPS designed for hiking/backpacking, and walked out your distances, it might be helpful. But, the velocity of a car totally queers your results.
posted by Netzapper at 4:23 PM on April 15

I'd agree with the poster who basically said you should learn from experience. Expose yourself to groups of people (OK, not THAT kind of "expose yourself") whose population size you are familar with, like classrooms, restaurants, clubs, and other small places. Then you can move on to larger sizes like stadiums and rallies.

For distances, I use my GPS. When I reach a mile, .8 miles, .4 miles, etc. from my destination, my GPS alerts me. As I drove, I started practicing figuring out on my own how far away an upcoming landmark was (such as a rock outcrop or grove of trees) and then seeing if I was right by checking the GPS. Now I am pretty good at guessing distance.
posted by Piscean at 9:07 AM on April 16