Estimation and Orders of Magnitude

I just read a blog post by Jonathan Claydon titled Year of Estimation. Like me, he's loving the site estimation180.com. I hadn't paid attention to how the items on the site build up from earlier to later, going from tissues in a travel pack to a box to a bigger package. I may use that feature if I can get myself using the site more often. (There's so much I'd like to do, and not enough time for it all.)

I make my own estimation activities too. This past week in pre-calc I brought in a jar of little origami stars and asked my students to estimate how many there were. This worked into Kate's absolute value lesson. After I announced the correct number of stars, I asked them each to write down how far off they were, their error. Of course some of them had to do Actual Number - Guess, or A-G, and others had to do G-A (leading us to absolute value). I put all the guesses on a spreadsheet, showed my students how I wrote a formula to have excel figure the error, and then graphed guess versus error, giving an absolute value graph. We decided that the good guesses were the ones with an error less than 20, giving us a reason to solve | 225 - x | < 20 (225 was the actual number of stars and x was the value of a guess).

Jonathan pointed to an online quiz that I found intriguing, on the relative sizes of things. I also found it frustrating, because with one wrong answer you had to start over. The quiz has some hard comparisons. Here are some I got wrong:  Which is bigger, ...

• the Eiffel Tower or the Great Pyramid of Gaza?
• the width of Uluru Rock (in Australia) or the height of Angel Falls in Venezuela?
• the Milky Way or the Crab Nebula?
• the moon or Pluto?
• Russia's east to west length or the moon's diameter?

I wanted an easier version - with only items my students would know about - that they could use to think about orders of magnitude. So I created one myself. I alphabetized so it would be easier to search the list, and I lettered them for easier reference. Are any on my list still hard? Could you add in any and keep it relatively easy? Where am I jumping the most between orders of magnitude?


Quiz Yourself on Estimation
Put these in order from smallest to largest.
a. blue whale
b. California
c. carbon atom
d. dog
e. Earth
f. egg
g. eiffel tower
h. electron
i. giraffe
j. human
k. Jupiter
l. Milky Way galaxy
m. moon
n. Mount Rushmore
o. Niagara Falls
p. Oregon
q. Pacific Ocean
r. proton
s. red blood cell
t. soccer ball
u. sun
v. sunflower seed
w. tennis ball
x. United States
y. water molecule
z. white house



If you are working on estimation or orders of magnitude, you may also like some of these resources:

• On Being the Right Size, by J.B.S. Haldane, originally published in The World of Mathematics, by James Newman
• Powers of Ten, by Philip and Phylis Morrison (youtube video here and the similar Universcale by Nikon here)
• Mathsemantics: Making Numbers Talk Sense, by Edward MacNeal (for the one great chapter on estimation)