Approximate Sizes Math Posters

How far is it from Boston to L.A.? How heavy is a gallon? 

I'm always on the lookout for great math history books, and recently picked up Innumeracy by John Allen Paulos. The way a book reads is really important to me. Even though I don't consider myself immumerate, I also know that math is infinite and I could study it all my life and never learn it all, so I like books that read in an approachable way. I liked the way a few test pages read, so brought the book home.

Innumeracy already had me hooked by the end of the updated preface. Then came this passage on page 8:

"I'm always amazed and depressed when I encounter students who have no idea what the approximate population of the United States is, or the approximate distance from coast to coast..." 

About how heavy is a cow? A car? How big is an ounce? How about a gram? Estimation has been hypothesized to be our "sixth sense", and when I think about it, some numbers are just really hard (for me, at least) to visualize. 

How much bigger is a billion than a million? Where's 1,000,000,000?

This immediately got me thinking about making some approximate sizes posters for students so that they have some easy, relatable images to reference. Most are customary measurements, but I've never not had to look up the size of a gram, so I threw in a raisin, too.

A gallon of water is about 8 pounds. A gallon of milk is a little heavier.

A pencil is about an ounce,

A raisin weighs around a gram,

A can of beans is about a pound,

And a larger car weighs around 2 tons.

This large cow caught me some flak from a farmer on Facebook. A 1-ton dairy cow is on the larger side of the range. Some cows weigh less than a ton, some weigh more. As an aside, my friend Karrie from Mrs. E Teaches Math recently visited a dairy farm and learned that cows produce 8-10 gallons of milk... per day!  I would have estimated 3 gallons. 

If you'd like the set of approximate sizes posters for your classroom, they are here in my dropbox

After posting on social media, I got some more book recommendations. I haven't read any of these yet except for Zero: The Biography of a Dangerous Idea, which is one of my ALL-TIME favorite books:

Infinite Powers by Steven Strogatz
Humble Pi by Matt Parker
Here's Looking at Euclid by Alex Bellos
Weapons of Math Destruction by Cathy O'Neil
Mathematics for Human Flourishing by Francis Su
The Housekeeper and the Professor by Yoko Ogawa
Building Thinking Classrooms in Mathematics by Peter Liljedahl
Pi in the Sky by John D. Burrow
The Joy of X by Steven Strogatz
Zero: The Biography of a Dangerous Idea by Charles Seife
How to Cut a Cake by Ian Stewart
100 Percent of Nothing (Black Brick Publishing) 
A History of Pi by Petr Beckmann

More posts:


  1. Dates and number lines also interest my students and me! We looked at the dates of pythagoras , the birth year of the USA and 2021 on a number line. Kids had no idea- the span of time

    1. Great idea. My daughter was talking last night about infinity hurting her brain. Timelines are other numbers that are hard to visualize. My favorite-- tyrannosaurus rex and present day are closer together on Earth's timeline than tyrannosaurus and stegosaurus.